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

Author

Jonathan Vos Post, Feb 15 2006

Keywords

• easy
• nonn

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

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

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.

Extensions

More terms from Harvey P. Dale, May 02 2019