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 A365680 #12 Sep 16 2023 02:21:29 %S A365680 1,2,2,3,2,4,2,4,3,4,2,6,2,4,4,4,2,6,2,6,4,4,2,8,3,4,4,6,2,8,2,5,4,4, %T A365680 4,9,2,4,4,8,2,8,2,6,6,4,2,8,3,6,4,6,2,8,4,8,4,4,2,12,2,4,6,6,4,8,2,6, %U A365680 4,8,2,12,2,4,6,6,4,8,2,8,4,4,2,12,4,4 %N A365680 The number of exponentially squarefree divisors of n. %C A365680 First differs from A252505 at n = 32. %C A365680 The number of divisors of n that are exponentially squarefree numbers (A209061), i.e., numbers having only squarefree exponents in their canonical prime factorization. %C A365680 The sum of these divisors is A365682(n) and the largest of them is A365683(n). %H A365680 Amiram Eldar, <a href="/A365680/b365680.txt">Table of n, a(n) for n = 1..10000</a> %F A365680 Multiplicative with a(p^e) = A013928(e+1) + 1. %F A365680 a(n) <= A000005(n), with equality if and only if n is a biquadratefree number (A046100). %t A365680 f[p_, e_] := Count[Range[e], _?SquareFreeQ] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A365680 (PARI) s(n) = sum(k=1, n, issquarefree(k)) + 1; %o A365680 a(n) = vecprod(apply(x -> s(x), factor(n)[, 2])); %Y A365680 Cf. A000005, A013928, A046100, A209061, A252505, A365682, A365683. %Y A365680 Similar sequences: A325837, A353898. %K A365680 nonn,easy,mult %O A365680 1,2 %A A365680 _Amiram Eldar_, Sep 15 2023