This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114446 #17 Feb 16 2025 08:32:59
%S A114446 27,43,96,107,128,147,180,187,203,224,288,312,336,352,360,387,392,395,
%T A114446 400,411,416,475,480,486,491,495,523,539,544,560,572,587,592,600,603,
%U A114446 619,621,627,635,704,729,735,752,763,779,795,800,810,819,840,843,882
%N A114446 Indices of 7-almost prime pentagonal numbers.
%C A114446 P(2) = 5 is the only prime pentagonal number, all other factor as P(k) = (k/2)*(3*k-1) or k*((3*k-1)/2) and thus have at least 2 prime factors. P(k) is semiprime iff [k prime and (3*k-1)/2 prime] or [k/2 prime and 3*k-1 prime].
%H A114446 Amiram Eldar, <a href="/A114446/b114446.txt">Table of n, a(n) for n = 1..10000</a>
%H A114446 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A114446 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>.
%F A114446 {a(n)} = {k such that A001222(A000326(k)) = 7}.
%F A114446 {a(n)} = {k such that k*(3*k-1)/2 has exactly 7 prime factors}.
%F A114446 {a(n)} = {k such that A000326(k) is an element of A046308}.
%e A114446 a(1) = 27 because P(27) = PentagonalNumber(27) = 27*(3*27-1)/2 = 1080 = 2^3 * 3^3 * 5 is a 7-almost prime.
%e A114446 a(2) = 43 because P(43) = 43*(3*43-1)/2 = 2752 = 2^6 * 43 is a 7-almost prime.
%e A114446 a(7) = 180 because P(180) = 180*(3*180-1)/2 = 48510 = 2 * 3^2 * 5 x 7^2 * 11 is a 7-almost prime.
%t A114446 Select[Range[2000],PrimeOmega[# (3#-1)/2]==7&] (* _Harvey P. Dale_, Jul 16 2011 *)
%Y A114446 Cf. A000326, A001222, A046308.
%K A114446 easy,nonn
%O A114446 1,1
%A A114446 _Jonathan Vos Post_, Feb 14 2006
%E A114446 More terms from _Harvey P. Dale_, Jul 16 2011