cp's OEIS Frontend

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.

A353152 Perfect powers that are divisible by 5.

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%I A353152 #55 Jul 02 2022 09:28:37
%S A353152 25,100,125,225,400,625,900,1000,1225,1600,2025,2500,3025,3125,3375,
%T A353152 3600,4225,4900,5625,6400,7225,8000,8100,9025,10000,11025,12100,13225,
%U A353152 14400,15625,16900,18225,19600,21025,22500,24025,25600,27000,27225,28900,30625
%N A353152 Perfect powers that are divisible by 5.
%C A353152 a(n) == 0 (mod 25).
%C A353152 a(n) == {0, 25, 75} (mod 100).
%H A353152 Michael De Vlieger, <a href="/A353152/b353152.txt">Table of n, a(n) for n = 1..10000</a>
%F A353152 a(n) = (5*m)^k for some positive m and some k > 1. - _David A. Corneth_, Apr 28 2022
%F A353152 Sum_{n>=1} 1/a(n) = -Sum_{k>=2} mu(k)*zeta(k)/5^k = 0.0756933503... - _Amiram Eldar_, Jul 02 2022
%e A353152 225 is a term since 225 = 15^2 is a power of a multiple of 5.
%t A353152 Select[Range[32000], And[GCD @@ FactorInteger[#][[All, 2]] > 1, Divisible[#, 5]] &] (* _Michael De Vlieger_, Apr 30 2022 *)
%o A353152 (PARI) isok(k) = ispower(k) && !(k%5); \\ _Michel Marcus_, Apr 27 2022
%o A353152 (PARI) upto(n) = { my(res = List()); forstep(i = 5, sqrtint(n), 5, c = i; for(e = 2, logint(n, i), c*=i; listput(res, c) ) ); Set(res) } \\ _David A. Corneth_, Apr 27 2022
%Y A353152 Cf. A000351, A011557.
%Y A353152 Intersection of A001597 and A008587.
%Y A353152 Cf. A075090 (even perfect powers).
%K A353152 nonn,easy
%O A353152 1,1
%A A353152 _Marco RipĂ _, Apr 26 2022