

A114558


Numbers n such that nth heptagonal number is 6almost prime.


1



15, 24, 27, 33, 48, 51, 55, 64, 71, 75, 81, 99, 105, 108, 111, 119, 120, 123, 126, 132, 141, 147, 150, 156, 160, 162, 171, 175, 177, 189, 198, 199, 204, 208, 215, 219, 222, 224, 249, 252, 258, 261, 263, 264, 267, 270, 272, 280, 285, 291, 294, 300, 304, 335
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OFFSET

1,1


COMMENTS

Hep(2) = 7 is the only prime heptagonal number.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Heptagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

n such that Hep(n) = n*(5*n3)/2 is 6almost prime. n such that A000566(n) is an element of A046306. n such that A001222(A000566(n)) = 6. n such that A001222(n*(5*n3)/2) = 6.


EXAMPLE

a(1) = 15 because Hep(15) = 15*(5*153)/2 = 540 = 2^2 * 3^3 * 5 is 6almost prime.
a(2) = 24 because Hep(24) = 24*(5*243)/2 = 1404 = 2^2 * 3^3 * 13.
a(7) = 55 because Hep(55) = 55*(5*553)/2 = 7480 = 2^3 * 5 * 11 * 17 is 6almost prime [also 7480 = Hep(55) = Hep(Hep(5)) is an iterated heptagonal number].
a(11) = 81 because Hep(81) = 81*(5*813)/2 = 16281 = 3^5 * 67 [also 16281 = Hep(81) = Hep(Hep(6)) is an iterated heptagonal number].
a(24) = 156 because Hep(156) = 156*(5*1563)/2 = 60606 = 2 * 3^2 * 7 * 13 * 37 is 6almost prime (and a palindrome).
a(30) = 189 because Hep(189) = 189*(5*1893)/2 = 89019 = 3^4 * 7 * 157 is 6almost prime [also 89019 = Hep(189) = Hep(Hep(9)) is an iterated heptagonal number].


MATHEMATICA

Select[Range[400], Total[Transpose[FactorInteger[# (5#3)/2]][[2]]]==6&] (* Harvey P. Dale, May 15 2011 *)


CROSSREFS

Cf. A000040, A000566, A001222, A001358, A046306.
Sequence in context: A274339 A343053 A114436 * A035408 A173035 A242152
Adjacent sequences: A114555 A114556 A114557 * A114559 A114560 A114561


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Feb 15 2006


EXTENSIONS

More terms from Harvey P. Dale, May 15 2011.


STATUS

approved



