Search: id:A007304
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%I A007304 M5207
%S A007304 30,42,66,70,78,102,105,110,114,130,138,154,165,170,174,182,186,190,195,
%T A007304 222,230,231,238,246,255,258,266,273,282,285,286,290,310,318,322,345,
%U A007304 354,357,366,370,374,385,399,402,406,410,418,426,429,430,434,435,438
%N A007304 Products of 3 distinct primes.
%C A007304 Also called sphenic numbers. Moebius function of n is -1. Note the distinctions 
               between this and "n has exactly three prime factors" or "n has exactly 
               three distinct prime factors." The word "sphenic" also means "shaped 
               like a wedge" [American Heritage Dictionary] as in dentation with 
               "sphenic molars." - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 
               11 2005
%C A007304 Also the volume of a sphenic brick. A sphenic brick is a rectangular 
               parallelopiped whose sides are components of a sphenic number, namely 
               whose sides are three distinct primes. Example: The distinct prime 
               triple (3,5,7) produces a 3x5x7 unit brick which has volume 105 cubic 
               units. 3-D analogue of 2-D A037074 Product of twin primes, per Cino 
               Hilliard's comment. Compare with 3-D A107768 Golden 3-almost primes 
               = Volumes of bricks (rectangular parallelopipeds) each of whose faces 
               has golden semiprime area. - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Jan 08 2007
%C A007304 Or the numbers n such that 13 = number of perfect partitions of n. - 
               Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 07 2009
%D A007304 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007304 "Sphenic", The American Heritage Dictionary of the English Language, 
               Fourth Edition, Houghton Mifflin Company, 2000.
%H A007304 T. D. Noe, <a href="b007304.txt">Table of n, a(n) for n=1..10000</a>
%F A007304 A000005(a(n)) = 8. [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 
               14 2009]
%F A007304 A002033(a(n)-1) = 13. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 07 2009, R. J. Mathar, Oct 14 2009]
%p A007304 a:=proc(n) if bigomega(n)=3 and nops(factorset(n))=3 then n else fi end: 
               seq(a(n),n=1..450); (Emeric Deutsch)
%t A007304 Union[Flatten[Table[Prime[n]*Prime[m]*Prime[k], {k, 20}, {n, k+1, 20}, 
               {m, n+1, 20}]]]
%t A007304 Take[ Sort@ Flatten@ Table[ Prime@i Prime@j Prime@k, {i, 3, 21}, {j, 
               2, i - 1}, {k, j - 1}], 53] (* Robert G. Wilson v *)
%Y A007304 Cf. A006881, A046386, A046387, A067885 (product of 2, 4, 5 and 6 distinct 
               primes, resp.)
%Y A007304 Cf. A046389, A046393, A061299, A067467, A071140, A096917, A096918, A096919, 
               A100765, A103653, A107464.
%Y A007304 Cf. A037074, A107768.
%Y A007304 Cf. A002033. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 
               10 2009]
%Y A007304 Sequence in context: A136152 A090815 A093599 this_sequence A160350 A053858 
               A075819
%Y A007304 Adjacent sequences: A007301 A007302 A007303 this_sequence A007305 A007306 
               A007307
%K A007304 nonn
%O A007304 1,1
%A A007304 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A007304 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 04 2006
%E A007304 Comment concerning number of divisors corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Aug 14 2009
%E A007304 Formula index corrected - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Oct 14 2009

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