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Search: id:A114554
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| A114554 |
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Numbers n such that n-th heptagonal number is 4-almost prime. |
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1
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| 6, 9, 12, 18, 21, 31, 35, 40, 44, 47, 49, 50, 56, 57, 65, 66, 76, 91, 107, 121, 125, 127, 129, 136, 138, 145, 148, 152, 154, 155, 163, 164, 187, 196, 201, 205, 212
(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 4-almost prime. n such that A000566(n) is an element of A014613. n such that A001222(A000566(n)) = 4. n such that A001222(n*(5*n-3)/2) = 4.
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EXAMPLE
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a(1) = 6 because Hep(6) = 6*(5*6-3)/2 = 81 = 3^4 is 4-almost prime.
a(2) = 9 because Hep(9) = 9*(5*9-3)/2 = 189 = 3^3 * 7 is 4-almost prime.
a(3) = 12 because Hep(12) = 12*(5*12-3)/2 = 342 = 2 * 3^2 * 19 is 4-almost prime.
a(4) = 18 because Hep(18) = 18*(5*18-3)/2 = 783 = 3^3 * 29 is 4-almost prime.
[also 783 = Hep(18) = Hep(Hep(3)) is the smallest 4-almost prime iterated heptagonal number].
a(11) = 49 because Hep(49) = 49*(5*49-3)/2 = 5929 = 7^2 * 11^2 is 4-almost prime (and the smallest such square heptagonal number A046196).
a(27) = 148 because Hep(148) = 148*(5*148-3)/2 = 54538 = 2 * 11 * 37 * 67 is 4-almost prime [also 54538 = Hep(148) = Hep(Hep(8)) is the second smallest 4-almost prime iterated heptagonal number].
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CROSSREFS
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Cf. A000040, A000566, A001222, A001358, A014613, A099153.
Adjacent sequences: A114551 A114552 A114553 this_sequence A114555 A114556 A114557
Sequence in context: A023042 A128245 A117714 this_sequence A023386 A036999 A118782
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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 15 2006
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