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Search: id:A114436
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| A114436 |
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Indices of 5-almost prime triangular numbers. |
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1
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| 15, 24, 27, 31, 35, 39, 44, 47, 54, 55, 56, 71, 72, 75, 79, 81, 84, 87, 90, 98, 107, 108, 112, 153, 155, 162, 164, 167, 170, 171, 174, 179, 180, 183, 184, 199, 203, 204, 209
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Eric Weisstein's World of Mathematics, Triangular Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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{a(n)} = {k such that A001222(A000217(k)) = 5}. {a(n)} = {k such that k*(k+1)/2 has exactly 5 prime factors, with multiplicity}. {a(n)} = {k such that A000217(k) is an element of A014614}.
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EXAMPLE
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a(1) = 15 because T(15) = TriangularNumber(15) = 15*(15+1)/2 = 120 = 2^3 * 3 * 5 is a 5-almost prime.
a(2) = 24 because T(24) = 24*(24+1)/2 = 300 = 2^2 * 3 * 5^2 is a 5-almost prime.
a(3) = 27 because T(27) = 27*(27+1)/2 = 378 = 2 * 3^3 * 7 is a 5-almost prime.
a(4) = 31 because T(27) = 31*(31+1)/2 = 496 = 2^4 * 31 is a 5-almost prime.
a(17) = 84 because T(27) = 84*(84+1)/2 = 3570 = 2 * 3 * 5 * 7 * 17 is a 5-almost prime.
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CROSSREFS
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Cf. A000217, A001222, A014614.
Adjacent sequences: A114433 A114434 A114435 this_sequence A114437 A114438 A114439
Sequence in context: A129387 A111151 A059144 this_sequence A114558 A035408 A081829
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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 13 2006
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