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 A381956 #11 Mar 12 2025 08:24:52
%S A381956 1,2,6,8,9,10,14,22,24,25,26,30,32,34,38,40,42,45,46,49,54,56,58,62,
%T A381956 63,66,70,72,74,75,78,81,82,86,88,94,96,99,102,104,106,108,110,114,
%U A381956 117,118,120,121,122,128,130,134,136,138,142,146,147,152,153,154,158,160
%N A381956 Numbers k such that k and the maximum exponent in the prime factorization of k have opposite parities.
%C A381956 Numbers k such that A000035(k) != A381955(k).
%C A381956 The asymptotic density of this sequence is 1/2 + Sum_{k>=2} ((-1)^(k+1)/((2^k-1)*zeta(k))) = 0.3753176676637566708086... .
%H A381956 Amiram Eldar, <a href="/A381956/b381956.txt">Table of n, a(n) for n = 1..10000</a>
%e A381956 2 is a term since 2 mod 2 = 0 and A051903(2) mod 2 = 1 mod 2 = 1 != 0.
%e A381956 4 is not a term since 4 mod 2 = 0 and also A051903(4) mod 2 = 2 mod 2 = 0.
%t A381956 q[k_] := If[k == 1, True, Mod[k, 2] != Mod[Max[FactorInteger[k][[;; , 2]]], 2]]; Select[Range[160], q]
%o A381956 (PARI) isok(k) = if(k == 1, 1, k % 2 != vecmax(factor(k)[,2]) % 2);
%Y A381956 Cf. A000035, A051903, A381955.
%Y A381956 Subsequences: A039956, A381950.
%K A381956 nonn,easy
%O A381956 1,2
%A A381956 _Amiram Eldar_, Mar 11 2025