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

%I A114559 #20 Feb 16 2025 08:32:59
%S A114559 60,63,72,114,144,159,167,180,183,207,216,225,247,255,275,297,312,315,
%T A114559 320,330,343,352,360,378,387,391,399,405,408,411,416,420,429,440,447,
%U A114559 448,450,459,465,468,483,486,504,513,520,525,531,546,588,591,594,609
%N A114559 Numbers k such that the k-th heptagonal number is 7-almost prime.
%H A114559 Amiram Eldar, <a href="/A114559/b114559.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Harvey P. Dale)
%H A114559 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A114559 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>.
%F A114559 Numbers k such that Hep(k) = k*(5*k-3)/2 is 7-almost prime.
%F A114559 Numbers k such that A000566(k) is a term of A046308.
%F A114559 Numbers k such that A001222(A000566(k)) = 7.
%F A114559 Numbers k such that A001222(k*(5*k-3)/2) = 7.
%e A114559 a(1) = 60 because Hep(60) = 60*(5*60-3)/2 = 8910 = 2 * 3^4 * 5 * 11 is 7-almost prime.
%e A114559 a(2) = 63 because Hep(63) = 63*(5*63-3)/2 = 9828 = 2^2 * 3^3 * 7 * 13 is 7-almost prime.
%e A114559 a(3) = 72 because Hep(72) = 72*(5*72-3)/2 = 12852 = 2^2 * 3^3 * 7 * 17 is 7-almost prime.
%e A114559 a(4) = 114 because Hep(114) = 114*(5*114-3)/2 = 32319 = 3^5 * 7 * 19 is 7-almost prime.
%t A114559 Select[Range[250],PrimeOmega[(#(5#-3))/2]==7&] (* _Harvey P. Dale_, May 02 2019 *)
%Y A114559 Cf. A000040, A000566, A001222, A001358, A046308.
%K A114559 easy,nonn
%O A114559 1,1
%A A114559 _Jonathan Vos Post_, Feb 15 2006
%E A114559 More terms from _Harvey P. Dale_, May 02 2019