0,3

For nonnegative n, partial sums of A057427 = Sign(n). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 2002

Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Oct 28 2008: (Start)

(APSO) Alternating partial sums of

(a-b+c-d+e-f+g...)=(a+b+c+d+e+f+g...)-2*(b+d+f...)

it appears that APSO A001477 =

A001057 = A000217 - 2*(A008794)

(End)

A001477 = A000040 U A141468. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 28 2009]

Or, zero together with natural numbers A000027; also A001477 = A002808 U A158611. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 27 2009]

Also, n minus smallest divisor of n; or A001477 = A005097 U A047845. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 09 2009]

Largest number<nth natural number. A001477 = A167706 U A167707. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 10 2009]

Contribution from Eric Desbiaux (moongerms(AT)wanadoo.fr), Nov 15 2009: (Start)

It appears that, with the Bachet-Bezout theorem, A001477 = (2*A080425) + (3*A008611)

and A000040 = (2*(3-A039701)) + (3*A157733) = 6 - 2*A039701 + 3*A157733,

implicating the Fundamental Theorem of Arithmetic.

(End)

Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.

N. J. A. Sloane, Table of n, a(n) for n = 0..500000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Tanya Khovanova, Recursive Sequences

Eric Weisstein's World of Mathematics, Natural Number

Eric Weisstein's World of Mathematics, Nonnegative Integer

Robert G. Wilson v, American English names for the numbers from 0 to 100999 without spaces or hyphens.

Index entries for "core" sequences

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences related to linear recurrences with constant coefficients

a(n)=n; a(0) = 0, a(n) = a(n-1)+1; G.f.: x/(1-x)^2.

Multiplicative with a(p^e) = p^e. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.

When seen as array: T(k, n) = n + (k+n)*(k+n+1)/2. Main diagonal is 2n(n+1) (A046092), antidiagonal sums are n(n+1)(n+2)/2 (A027480). - Ralf Stephan, Oct 17 2004

Dirichlet generating function: zeta(s-1). - Franklin T. Adams-Watters, Sep 11 2005.

E.g.f. x*e^x. - Franklin T. Adams-Watters, Sep 11 2005.

a(0)=0, a(1)=1, a(n)=2a(n-1)-a(n-2). - Jaume Oliver i Lafont (joliverlafont(AT)gmail.com), May 07 2008

a(n)=n-1 for n>0. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Sep 27 2009]

a(n)=A000027(n)-A000012(n). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 09 2009]

[ seq(n, n=0..100) ];

Table[n, {n, 0, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006

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

(Other) sage: [log(e^n)for n in xrange(0, 78)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2009]

(PARI) A001477(n)=n /* first term is a(0) */

Cf. A000027.

Sequence in context: A119972 A131738 A000027 this_sequence A087156 A033619 A130734

Adjacent sequences: A001474 A001475 A001476 this_sequence A001478 A001479 A001480

core,nonn,easy,mult,tabl,new

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

Duplicate formula removed by Michael Porter (michael_b_porter(AT)yahoo.com), Nov 02 2009