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 A096156 #29 Dec 20 2021 10:01:13 %S A096156 12,20,28,44,45,52,63,68,76,92,99,116,117,124,148,153,164,171,172,175, %T A096156 188,207,212,236,244,261,268,275,279,284,292,316,325,332,333,356,369, %U A096156 387,388,404,412,423,425,428,436,452,475,477,508,524,531,539,548,549 %N A096156 Numbers with ordered prime signature (2,1). %C A096156 Numbers of the form p^2 * q where p and q are primes with p < q. %C A096156 Also terms of A054753 that are not in A095990. %C A096156 There are pairs that differ by 1, which is not the case in A095990, beginning with 44 and 45, 116 and 117, 171 and 172, 332 and 333, etc. %H A096156 Enrique Pérez Herrero, <a href="/A096156/b096156.txt">Table of n, a(n) for n = 1..5000</a> %H A096156 OEIS Wiki, <a href="http://oeis.org/wiki/Ordered_prime_signatures">Ordered prime signatures</a> %e A096156 a(2) = 20 because 20 = 2*2*5 and 2 < 5. %e A096156 Note that 18 = 2*3^2 is not in the sequence, even though it has prime signature (2,1), because its ordered prime signature is (1,2) (A095990). Prime signatures correspond to partitions of Omega(n), while ordered prime signatures correspond to compositions of Omega(n). %t A096156 Take[ Sort[ Flatten[ Table[ Prime[p]^2 Prime[q], {q, 2, 33}, {p, q - 1}]]], 54] (* _Robert G. Wilson v_, Jul 28 2004 *) %t A096156 Select[Range[10^5],FactorInteger[#][[All,2]]=={2,1}&] (* _Enrique Pérez Herrero_, Jun 27 2012 *) %o A096156 (PARI) list(lim)=my(v=List()); forprime(q=3, lim\4, forprime(p=2, min(sqrtint(lim\q), q-1), listput(v, p^2*q))); Set(v) \\ _Charles R Greathouse IV_, Feb 26 2014 %o A096156 (Python) %o A096156 from sympy import factorint %o A096156 def ok(n): return list(factorint(n).values()) == [2, 1] %o A096156 print([k for k in range(550) if ok(k)]) # _Michael S. Branicky_, Dec 20 2021 %Y A096156 Cf. A095990. %Y A096156 Subsequence of A054753, A097320, A325241, A345381. %K A096156 nonn,easy %O A096156 1,1 %A A096156 _Alford Arnold_, Jul 24 2004 %E A096156 Edited and extended by _Robert G. Wilson v_ and _Rick L. Shepherd_, Jul 27 2004