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A114558 Numbers n such that n-th heptagonal number is 6-almost 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 31 02:09 EDT 2021. Contains 346366 sequences. (Running on oeis4.)