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 A351663 #22 Jul 02 2022 09:28:43 %S A351663 49,196,343,441,784,1225,1764,2401,2744,3136,3969,4900,5929,7056,8281, %T A351663 9261,9604,11025,12544,14161,15876,16807,17689,19600,21609,21952, %U A351663 23716,25921,28224,30625,33124,35721,38416,41209,42875,44100,47089,50176,53361,56644 %N A351663 Perfect powers that are divisible by 7. %C A351663 Terms are multiples of 49, since no perfect power divisible by 7 can have a 7-adic valuation below 2. %H A351663 Amiram Eldar, <a href="/A351663/b351663.txt">Table of n, a(n) for n = 1..10000</a> %F A351663 a(n) has the form (7*m)^k for some m > 0 and k > 1. %F A351663 Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/7^k = 0.0371288923... - _Amiram Eldar_, Jul 02 2022 %e A351663 196 is a term since 196 = (2*7)^2 is a power of a multiple of 7. %p A351663 q:= n-> igcd(seq(i[2], i=ifactors(n)[2]))>1: %p A351663 select(q, [49*i$i=1..2000])[]; # _Alois P. Heinz_, May 05 2022 %t A351663 Select[49*Range[1200], GCD @@ FactorInteger[#][[All, 2]] > 1 &] %o A351663 (PARI) isok(k) = ispower(k) && !(k % 7) %Y A351663 Intersection of A001597 and A008589. %Y A351663 Other perfect powers: A075090, A075109, A353238, A353152. %K A351663 nonn,easy %O A351663 1,1 %A A351663 _Marco RipĂ _, May 04 2022