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 A114447 Indices of 6-almost 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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]. LINKS 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*k-1)/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*32-1)/2 = 1520 = 2^4 * 5 * 19 is a 6-almost prime. a(3) = 64 because P(64) = 64*(3*64-1)/2 = 6112 = 2^5 * 191 is a 6-almost prime. a(15) = 144 because P(144) = 144*(3*144-1)/2 = 31032 = 2^3 * 3^2 * 431 is a 6-almost 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

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Last modified October 18 14:52 EDT 2019. Contains 328161 sequences. (Running on oeis4.)