A114558 Numbers k such that the k-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

Author

Jonathan Vos Post, Feb 15 2006

Keywords

• nonn
• easy

Examples

			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].
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)
• Eric Weisstein's World of Mathematics, Almost Prime.
• Eric Weisstein's World of Mathematics, Heptagonal Number.

Crossrefs

Cf. A000040, A000566, A001222, A001358, A046306.

Programs

Mathematica

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

Formula

Numbers k such that Hep(k) = k*(5*k-3)/2 is 6-almost prime.

Numbers k such that A000566(k) is a term of A046306.

Numbers k such that A001222(A000566(k)) = 6.

Numbers k such that A001222(k*(5*k-3)/2) = 6.

Extensions

More terms from Harvey P. Dale, May 15 2011