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 A061680 #23 Dec 02 2023 09:12:55 %S A061680 1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,3,1,1,1,1,1,1,1,3,1,1,1,1,1,1, %T A061680 1,1,1,1,1,1,1,1,1,3,3,1,1,1,1,3,1,3,1,1,1,1,1,1,1,3,1,1,3,1,1,1,1,3, %U A061680 1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,3,1,1,1,1,1,3,1,3,1,1,1,3,1,3,3,1,1,1,1,1,1 %N A061680 a(n) = gcd(d(n^2), d(n)). %H A061680 Amiram Eldar, <a href="/A061680/b061680.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..2000 from Harry J. Smith) %F A061680 a(n) = gcd(A000005(A000290(n)), A000005(n)) = gcd(A048691(n), A000005(n)). %e A061680 This GCD can only be odd since d(n^2) is odd. %e A061680 For n = 4608: a(4608) = gcd(d(21233664), d(4608)) = gcd(95, 30) = 5. %t A061680 Table[GCD[DivisorSigma[0,n],DivisorSigma[0,n^2]],{n,110}] (* _Harvey P. Dale_, Sep 03 2023 *) %o A061680 (PARI) a(n) = gcd(numdiv(n^2), numdiv(n)); \\ _Harry J. Smith_, Jul 26 2009 %o A061680 (PARI) a(n) = {my(e = factor(n)[,2]); gcd(vecprod(apply(x -> 2*x+1, e)), vecprod(apply(x -> x+1, e)));} \\ _Amiram Eldar_, Dec 02 2023 %Y A061680 Cf. A000005, A000290, A048691. %K A061680 nonn %O A061680 1,12 %A A061680 _Labos Elemer_, Jun 18 2001 %E A061680 Offset changed from 0 to 1 by _Harry J. Smith_, Jul 26 2009