0,1

Number of ways of writing n as a product of primes.

Number of ways of writing n as a sum of distinct powers of 2.

Continued fraction for golden ratio A001622.

Partial sums of A000007 (characteristic function of 0). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 2002

An example of an infinite sequence of positive integers whose distinct pairwise concatenations are all primes! - Don Reble, Apr 17 2005

Binomial transform of A000007; inverse binomial transform of A000079 . Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 07 2005

A063524(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 11 2008]

For n >= 0, let M(n) be the matrix with 1st row = (n n+1) and 2nd row = (n+1 n+2). Then a(n) = absolute value of det(M(n)). [From Kailasam Viswanathan Iyer (kvi(AT)nitt.edu), Apr 11 2009]

The partial sums give the natural numbers (A000027). [From Daniel Forgues (squid(AT)zensearch.com), May 08 2009]

Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 04 2009: (Start)

a(n) is also tau_1(n) where tau_2(n) is A000005

a(n) is a completely multiplicative arithmetical function.

a(n) is both square free and a perfect square. See A005117 and A000290. (End)

Also smallest divisor of n. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 07 2009].

a(n) is also the decimal expansion of 10/9 [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 18 2009]

a(n) is also the number of complete graphs on n nodes. [From Pablo Chavez (pchavez(AT)cmu.edu), Sep 15 2009]

Totally multiplicative sequence with a(p) = 1 for prime p. Totally multiplicative sequence with a(p) = a(p-1) for prime p. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 18 2009]

nth prime minus phi(prime(n)); number of divisors of n-th prime minus number of perfect partitions of n-th prime; the number of perfect partitions of n-th prime number; the number of perfect partitions of n-th non-composite number. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 26 2009]

Contribution from Harlan J. Brothers (harlan(AT)brotherstechnology.com), Nov 01 2009: (Start)

For all n>0, the sequence of limit values for a(n)=n!Sum[k=n..inf, k/(k+1)! ]

Also, for all n != 0, a(n)=n^0 (End)

a(n) is also the number of 0-regular graphs on n vertices. [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Nov 07 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Michael Z. Spivey and Laura L. Steil, The k-Binomial Transforms and the Hankel Transform, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

N. J. A. Sloane, Table of n, a(n) for n = 0..1000 [Useful when plotting one sequence against another. See Swayne link.]

Index entries for sequences related to linear recurrences with constant coefficients

Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.

N. J. A. Sloane, Illustration of initial terms

D. F. Swayne, Plot pairs of sequences in the OEIS

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics

Eric Weisstein's World of Mathematics, Chromatic Number

Eric Weisstein's World of Mathematics, Graph Cycle

G. Xiao, Contfrac

Index entries for "core" sequences

Index entries for characteristic functions

Index entries for continued fractions for constants

Index entries for related partition-counting sequences

Harlan Brothers, Factorial: Summation (formula 06.01.23.0002), The Wolfram Functions Site [From Harlan J. Brothers (harlan(AT)brotherstechnology.com), Nov 01 2009]

G.f.: 1/(1-x); a(n)=1. E.g.f.: e^x.

G.f.: Product[(1+x^(2^k)),{k,0,Infinity}]. - Zak Seidov (zakseidov(AT)yahoo.com), Apr 06 2007

Multiplicative with a(p^e) = 1.

Dirichlet generating function: zeta(s). - Franklin T. Adams-Watters, Sep 11 2005.

Regarded as a square array by antidiagonals, g.f. 1/((1-x)(1-y)), e.g.f. sum T(n,m) x^n/n! y^m/m! = e^{x+y}, e.g.f. sum T(n,m) x^n y^m/m! = e^y/(1-x). Regarded as a triangular array, g.f. 1/((1-x)(1-xy)), e.g.f. sum T(n,m) x^n y^m/m! = e^{xy}/(1-x). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Feb 06 2006

Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 04 2009: (Start)

a(n)=Sum(d|n,mu(n/d)*tau_2(d))=1, where tau_2(n)=A000005 and mu(n)=A008683

a(n)=|Sum(d|n,mu(d)*tau_2(d))|=1 (End)

a(n)=A000027(n)-A001477(n). - Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 09 2009

a(n)=A002033(A000040(n))=A002033(A008578(n))=A000005(A000040(n))-A002033(n)=A000027(A000040(n))-A000010(A000040(n)). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 26 2009]

1.618033988749894848204586834... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]

A000012 := n->1;

[ seq(1, i=0..100) ];

a[n_] := 1

Array[1 &, 50] - Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 26 2006

Table[n!Sum[k/(k+1)!, {k, n, \[Infinity]}], {n, 10}] [From Harlan J. Brothers (harlan(AT)brotherstechnology.com), Nov 01 2009]

(MAGMA) [ 1 : n in [0..100]];

(PARI) a(n)=1

(PARI) { default(realprecision, 1080); phi = (1 + sqrt(5))/2; x=contfrac(phi); for (n=1, 1001, write("b000012.txt", n-1, " ", x[n])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 14 2009]

Cf. A000004, A007395, A010701.

Cf. A000027.

Cf. tau_2(n): A000005, tau_3(n): A007425, tau_4(n): A007426, tau_5(n): A061200, tau_6(n): A034695, (unordered) 2-factorizations of n: A038548, (unordered) 3-factorizations of n: A034836, A001055, (tau<=)_2(n): A006218, (tau<=)_3(n): A061201, (tau<=)_5(n): A061203, (tau<=)_6(n): A061204. [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Sep 04 2009]

Cf. A000010, A000040, A002033, A008578. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 26 2009]

Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7). [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Nov 07 2009]

Sequence in context: A087960 A164660 A114523 this_sequence A008836 A064179 A106400

Adjacent sequences: A000009 A000010 A000011 this_sequence A000013 A000014 A000015

core,easy,nonn,mult,cofr,tabl,new

N. J. A. Sloane (njas(AT)research.att.com).