A114558 Numbers n such that n-th heptagonal number is 6-almost prime.

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

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*n-3)/2 is 6-almost prime. n such that A000566(n) is an element of A046306. n such that A001222(A000566(n)) = 6. n such that A001222(n*(5*n-3)/2) = 6.

Example

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