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%I #6 Mar 30 2012 18:40:35
%S 32,48,64,72,81,91,99,108,112,117,123,135,139,144,152,155,160,162,176,
%T 195,207,208,216,219,240,252,264,272,275,279,292,297,300
%N Indices of 6-almost prime pentagonal numbers.
%C P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>
%F {a(n)} = {k such that A001222(A000326(k)) = 6}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 6 prime factors}. {a(n)} = {k such that A000326(k) is an element of A046306}.
%e a(1) = 32 because P(32) = PentagonalNumber(32) = 32*(3*32-1)/2 = 1520 = 2^4 * 5 * 19 is a 6-almost prime.
%e a(3) = 64 because P(64) = 64*(3*64-1)/2 = 6112 = 2^5 * 191 is a 6-almost
%e prime.
%e a(15) = 144 because P(144) = 144*(3*144-1)/2 = 31032 = 2^3 * 3^2 * 431 is a 6-almost prime.
%Y Cf. A000326, A001222, A046306.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 14 2006
%E 82 removed by R. J. Mathar, Dec 22 2010
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