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Search: id:A114556
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| A114556 |
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Numbers n such that n-th heptagonal number is 5-almost prime. |
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1
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| 7, 16, 23, 30, 36, 42, 45, 54, 69, 78, 79, 80, 84, 88, 90, 93, 95, 100, 102, 104, 112, 115, 117, 140, 143, 151, 153, 170, 174, 176, 184, 186, 191, 200, 203, 210
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Hep(2) = 7 is the only prime heptagonal number.
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LINKS
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Eric Weisstein's World of Mathematics, Heptagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
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FORMULA
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n such that Hep(n) = n*(5*n-3)/2 is 5-almost prime. n such that A000566(n) is an element of A014614. n such that A001222(A000566(n)) = 5. n such that A001222(n*(5*n-3)/2) = 5.
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EXAMPLE
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a(1) = 7 because Hep(7) = 7*(5*7-3)/2 = 112 = 2^4 * 7 is 5-almost prime [also 112 = Hep(7) = Hep(Hep(2)) is an iterated heptagonal number].
a(2) = 16 because Hep(16) = 16*(5*16-3)/2 = 616 = 2^3 * 7 * 11 is 5-almost prime.
a(3) = 23 because Hep(23) = 23*(5*23-3)/2 = 1288 = 2^3 * 7 * 23.
a(18) = 100 because Hep(100) = 100*(5*100-3)/2 = 24850 = 2 * 5^2 * 7 * 71.
a(21) = 112 because Hep(112) = 112*(5*112-3)/2 = 31192 = 2^3 * 7 * 557 [also 31192 = Hep(112) = Hep(Hep(7)) = Hep(Hep(Hep(2))) is an iterated heptagonal number].
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CROSSREFS
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Cf. A000040, A000566, A001222, A001358, A014614.
Sequence in context: A060914 A044059 A044440 this_sequence A136772 A043481 A017245
Adjacent sequences: A114553 A114554 A114555 this_sequence A114557 A114558 A114559
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 15 2006
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