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 A097273 #18 May 22 2025 17:45:26
%S A097273 1,2,3,4,6,8,9,12,15,16,18,24,27,30,32,36,45,48,54,60,64,72,81,90,96,
%T A097273 105,108,120,128,135,144,162,180,192,210,216,225,240,243,256,270,288,
%U A097273 315,324,360,384,405,420,432,450,480,486,512,540,576,630,648,675,720
%N A097273 Least integer with each "mod 2 prime signature".
%C A097273 For n = 2^e_0 * p_1^e_1 * ... * p_n^e_n where p_i is odd prime and e_1 >= e_2 >= ... >= e_n, define "mod 2 prime signature" to be ordered prime exponents (e_0,e_1,...,e_n).
%C A097273 Least integer with a given mod 2 prime signature is obtained by replacing p_1 with 3, p_2 with 5,..., p_n with n-th odd prime.
%C A097273 A097272 sorted and duplicates removed.
%C A097273 Numbers k such that A097272(k) = k.
%C A097273 Verified up to a(68) = 972, 2*a(n) is also the order of a dihedral group D such that the lattice of normal subgroups of D is not isomorphic to the lattice of normal subgroups of any dihedral group of order less than 2*a(n). - _Miles Englezou_, May 18 2025
%H A097273 Amiram Eldar, <a href="/A097273/b097273.txt">Table of n, a(n) for n = 1..10000</a>
%F A097273 Sum_{n>=1} 1/a(n) = 2 * Product_{n>=2} 1/(1 - 1/A070826(n)) = 3.2482341898... . - _Amiram Eldar_, Jul 23 2024
%t A097273 lpsQ[n_] := n==1 || (Max@ Differences[(f = FactorInteger[n])[[;;,2]]] < 1 && f[[-1,1]] == Prime[Length[f] + 1]); Select[Range[1000], lpsQ[# / 2^IntegerExponent[#, 2]] &] (* _Amiram Eldar_, Jul 23 2024 *)
%Y A097273 Cf. A097272, A097274, A097275.
%Y A097273 Cf. A025487, A070826, A147516.
%K A097273 nonn
%O A097273 1,2
%A A097273 _Ray Chandler_, Aug 22 2004
%E A097273 Offset corrected by _Amiram Eldar_, Jul 23 2024