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Search: id:A114443
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| A114443 |
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Indices of 4-almost prime pentagonal numbers. |
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+0
1
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| 12, 15, 16, 19, 24, 33, 36, 39, 45, 47, 52, 55, 56, 57, 60, 68, 70, 77, 83, 84, 88, 90, 95, 102, 103, 104, 105, 110, 111, 114, 119, 124, 127, 138, 140, 142, 143, 145, 150, 153, 156, 163, 169, 172, 177, 179
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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].
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LINKS
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Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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{a(n)} = {k such that A001222(A000326(k)) = 3}. {a(n)} = {k such that k*(3*k-1)/2 has exactly 3 prime factors}. {a(n)} = {k such that A000326(k) is an element of A014613}.
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EXAMPLE
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a(1) = 12 because P(12) = PentagonalNumber(12) = 12*(3*12-1)/2 = 210 = 2 * 3 * 5 * 7 is a 4-almost prime In fact the primorial 4#).
a(3) = 16 because P(16) = 16*(3*16-1)/2 = 376 = 2^3 * 47 is a 4-almost
prime (the prime factors need not be distinct).
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CROSSREFS
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Cf. A000326, A001222, A014613, A115709.
Sequence in context: A002926 A139310 A115402 this_sequence A101171 A120169 A115349
Adjacent sequences: A114440 A114441 A114442 this_sequence A114444 A114445 A114446
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 14 2006
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