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A114554
Numbers k such that the k-th heptagonal number is 4-almost prime.
1
6, 9, 12, 18, 21, 31, 35, 40, 44, 47, 49, 50, 56, 57, 65, 66, 76, 91, 107, 121, 125, 127, 129, 136, 138, 145, 148, 152, 154, 155, 163, 164, 187, 196, 201, 205, 212, 220, 221, 223, 226, 230, 235, 236, 237, 239, 242, 246, 248, 260, 268, 284, 289, 292, 299, 309
OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 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 4-almost prime.
Numbers k such that A000566(k) is a term of A014613.
Numbers k such that A001222(A000566(k)) = 4.
Numbers k such that A001222(k*(5*k-3)/2) = 4.
EXAMPLE
a(1) = 6 because Hep(6) = 6*(5*6-3)/2 = 81 = 3^4 is 4-almost prime.
a(2) = 9 because Hep(9) = 9*(5*9-3)/2 = 189 = 3^3 * 7 is 4-almost prime.
a(3) = 12 because Hep(12) = 12*(5*12-3)/2 = 342 = 2 * 3^2 * 19 is 4-almost prime.
a(4) = 18 because Hep(18) = 18*(5*18-3)/2 = 783 = 3^3 * 29 is 4-almost prime.
[also 783 = Hep(18) = Hep(Hep(3)) is the smallest 4-almost prime iterated heptagonal number].
a(11) = 49 because Hep(49) = 49*(5*49-3)/2 = 5929 = 7^2 * 11^2 is 4-almost prime (and the smallest such square heptagonal number A046196).
a(27) = 148 because Hep(148) = 148*(5*148-3)/2 = 54538 = 2 * 11 * 37 * 67 is 4-almost prime [also 54538 = Hep(148) = Hep(Hep(8)) is the second smallest 4-almost prime iterated heptagonal number].
MATHEMATICA
Select[Range[500], PrimeOmega[(#(5#-3))/2]==4&] (* Harvey P. Dale, Aug 04 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 15 2006
EXTENSIONS
More terms from Harvey P. Dale, Aug 04 2016
STATUS
approved