

A114447


Indices of 6almost prime pentagonal numbers.


0



32, 48, 64, 72, 81, 91, 99, 108, 112, 117, 123, 135, 139, 144, 152, 155, 160, 162, 176, 195, 207, 208, 216, 219, 240, 252, 264, 272, 275, 279, 292, 297, 300
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OFFSET

1,1


COMMENTS

P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k1) or k*((3*k1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k1)/2 prime] or [k/2 prime and 3*k1 prime].


LINKS

Table of n, a(n) for n=1..33.
Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

{a(n)} = {k such that A001222(A000326(k)) = 6}. {a(n)} = {k such that k*(3*k1)/2 has exactly 6 prime factors}. {a(n)} = {k such that A000326(k) is an element of A046306}.


EXAMPLE

a(1) = 32 because P(32) = PentagonalNumber(32) = 32*(3*321)/2 = 1520 = 2^4 * 5 * 19 is a 6almost prime.
a(3) = 64 because P(64) = 64*(3*641)/2 = 6112 = 2^5 * 191 is a 6almost
prime.
a(15) = 144 because P(144) = 144*(3*1441)/2 = 31032 = 2^3 * 3^2 * 431 is a 6almost prime.


CROSSREFS

Cf. A000326, A001222, A046306.
Sequence in context: A271784 A114416 A046304 * A090052 A163285 A036329
Adjacent sequences: A114444 A114445 A114446 * A114448 A114449 A114450


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 14 2006


EXTENSIONS

82 removed by R. J. Mathar, Dec 22 2010


STATUS

approved



