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 A114445 #15 Feb 16 2025 08:32:59
%S A114445 11,35,40,42,51,54,59,63,67,80,87,92,100,115,120,125,126,131,132,136,
%T A114445 159,165,167,168,175,184,189,200,204,210,215,217,222,225,227,231,232,
%U A114445 242,247,250,251,255,259,260,261,270,280,282,283,285,287,291,295,304,306
%N A114445 Indices of 5-almost prime pentagonal numbers.
%C A114445 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 A114445 Amiram Eldar, <a href="/A114445/b114445.txt">Table of n, a(n) for n = 1..10000</a>
%H A114445 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A114445 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>.
%F A114445 {a(n)} = {k such that A001222(A000326(k)) = 5}.
%F A114445 {a(n)} = {k such that k*(3*k-1)/2 has exactly 5 prime factors}.
%F A114445 {a(n)} = {k such that A000326(k) is an element of A014614}.
%e A114445 a(1) = 11 because P(11) = PentagonalNumber(11) = 11*(3*11-1)/2 = 176 = 2^4 * 11 is a 4-almost prime (the prime factors need not be distinct).
%e A114445 a(2) = 35 because P(35) = 35*(3*35-1)/2 = 1820 = 2^2 * 5 * 7 * 13 is a 5-almost prime.
%e A114445 a(13) = 100 because P(100) = 100*(3*100-1)/2 = 14950 = 2 * 5^2 * 13 * 23 is a 5-almost prime.
%t A114445 Select[Range[300], PrimeOmega[PolygonalNumber[5, #]] == 5 &] (* _Amiram Eldar_, Oct 05 2024 *)
%Y A114445 Cf. A000326, A001222, A014614.
%K A114445 easy,nonn
%O A114445 1,1
%A A114445 _Jonathan Vos Post_, Feb 14 2006
%E A114445 More terms from _Amiram Eldar_, Oct 05 2024