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A114559
Numbers k such that the k-th heptagonal number is 7-almost prime.
1
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 15 2006
EXTENSIONS
More terms from Harvey P. Dale, May 02 2019
STATUS
approved