A114559 Numbers k such that the k-th heptagonal number is 7-almost prime.

60, 63, 72, 114, 144, 159, 167, 180, 183, 207, 216, 225, 247, 255, 275, 297, 312, 315, 320, 330, 343, 352, 360, 378, 387, 391, 399, 405, 408, 411, 416, 420, 429, 440, 447, 448, 450, 459, 465, 468, 483, 486, 504, 513, 520, 525, 531, 546, 588, 591, 594, 609

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2000 from Harvey P. Dale)

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Heptagonal Number.

Formula

Numbers k such that Hep(k) = k*(5*k-3)/2 is 7-almost prime.

Numbers k such that A000566(k) is a term of A046308.

Numbers k such that A001222(A000566(k)) = 7.

Numbers k such that A001222(k*(5*k-3)/2) = 7.

Example

a(1) = 60 because Hep(60) = 60*(5*60-3)/2 = 8910 = 2 * 3^4 * 5 * 11 is 7-almost prime.
a(2) = 63 because Hep(63) = 63*(5*63-3)/2 = 9828 = 2^2 * 3^3 * 7 * 13 is 7-almost prime.
a(3) = 72 because Hep(72) = 72*(5*72-3)/2 = 12852 = 2^2 * 3^3 * 7 * 17 is 7-almost prime.
a(4) = 114 because Hep(114) = 114*(5*114-3)/2 = 32319 = 3^5 * 7 * 19 is 7-almost prime.

Mathematica

Select[Range[250], PrimeOmega[(#(5#-3))/2]==7&] (* Harvey P. Dale, May 02 2019 *)

Crossrefs

Cf. A000040, A000566, A001222, A001358, A046308.

Sequence in context: A256749 A280183 A181463 * A175102 A344811 A295697

Adjacent sequences: A114556 A114557 A114558 * A114560 A114561 A114562

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 15 2006

Extensions

More terms from Harvey P. Dale, May 02 2019

Status

approved