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 A056555 #20 Oct 27 2022 07:32:04 %S A056555 1,8,27,4,125,216,343,2,9,1000,1331,108,2197,2744,3375,1,4913,72,6859, %T A056555 500,9261,10648,12167,54,25,17576,3,1372,24389,27000,29791,8,35937, %U A056555 39304,42875,36,50653,54872,59319,250,68921,74088,79507,5324,1125 %N A056555 Smallest number k (k>0) such that n*k is a perfect 4th power. %H A056555 Amiram Eldar, <a href="/A056555/b056555.txt">Table of n, a(n) for n = 1..10000</a> %H A056555 Henry Bottomley, <a href="http://fs.gallup.unm.edu/Bottomley-Sm-Mult-Functions.htm">Some Smarandache-type multiplicative sequences</a>. %F A056555 a(n) = A053167(n)/n = n^3/A000190(n)^4 = A056553(n)/A053165(n). %F A056555 Multiplicative with a(p^e) = p^((4 - e) mod 4). - _Amiram Eldar_, Sep 08 2020 %F A056555 Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(16)/(4*zeta(4))) * Product_{p prime} (1 - 1/p^2 + 1/p^4 - 1/p^7 + 1/p^8) = 0.1537848996... . - _Amiram Eldar_, Oct 27 2022 %e A056555 a(64) = 4 because the smallest 4th power divisible by 64 is 256 and 64*4 = 256. %t A056555 f[p_, e_] := p^Mod[4 - e, 4]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* _Amiram Eldar_, Sep 08 2020 *) %o A056555 (PARI) a(n,f=factor(n))=f[,2]=-f[,2]%4; factorback(f) \\ _Charles R Greathouse IV_, Apr 24 2020 %Y A056555 Cf. A000190, A008835, A048798, A053164, A053165, A053166, A053167, A056554. %Y A056555 Cf. A013662, A013674. %K A056555 nonn,mult %O A056555 1,2 %A A056555 _Henry Bottomley_, Jun 25 2000