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 A377821 #12 Nov 09 2024 16:18:12
%S A377821 1,4,8,9,16,25,27,32,36,49,64,72,81,100,108,121,125,128,144,169,196,
%T A377821 200,225,243,256,288,289,324,343,361,392,400,432,441,484,500,512,529,
%U A377821 576,625,648,675,676,729,784,800,841,900,961,968,972,1024,1089,1125,1152
%N A377821 Powerful numbers that have no more than one odd exponent in their prime factorization.
%C A377821 Powerful numbers k such that A350389(k) is either 1 or a prime power with an odd exponent (A246551).
%H A377821 Amiram Eldar, <a href="/A377821/b377821.txt">Table of n, a(n) for n = 1..10000</a>
%H A377821 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%F A377821 Sum_{n>=1} 1/a(n) = zeta(2) * (1 + P(3)) = A013661 * (1 + A085541) = 1.93240708584418977513... .
%t A377821 With[{max = 1200}, Select[Union@ Flatten@Table[i^2 * j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}], # == 1 || Count[FactorInteger[#][[;; , 2]], _?OddQ] <= 1 &]]
%o A377821 (PARI) is(k) = if(k == 1, 1, my(e = factor(k)[, 2]); vecmin(e) > 1 && #select(x -> (x%2), e) <= 1);
%Y A377821 Disjoint union of A000290 \ {0} and A377820.
%Y A377821 Cf. A013661, A085541, A246551, A350389.
%K A377821 nonn,easy
%O A377821 1,2
%A A377821 _Amiram Eldar_, Nov 09 2024