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 A365683 #11 Jul 07 2025 04:06:02
%S A365683 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,8,17,18,19,20,21,22,23,24,25,26,
%T A365683 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,24,49,
%U A365683 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68
%N A365683 The largest exponentially squarefree divisor of n.
%C A365683 First differs from A058035 at n = 32.
%C A365683 The number of these divisors is A365680(n) and their sum is A365682(n).
%H A365683 Amiram Eldar, <a href="/A365683/b365683.txt">Table of n, a(n) for n = 1..10000</a>
%F A365683 Multiplicative with a(p^e) = p^A070321(e).
%F A365683 a(n) <= n, with equality if and only if n is exponentially squarefree number (A209061).
%F A365683 Sum_{k=1..n} a(k) ~ c*n^2, where c = 0.487850776747... = (1/2) * Product_{p prime} (1 + Sum_{k>=1} (p^f(k) - p^(f(k-1)+1))/p^(2*k)), f(k) = A070321(k) and f(0) = 0.
%t A365683 f[p_, e_] := Module[{k = e}, While[! SquareFreeQ[k], k--]; p^k]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A365683 (PARI) s(e) = {my(k = e); while(!issquarefree(k), k--); k;};
%o A365683 a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^s(f[i,2]));}
%Y A365683 Cf. A070321, A209061, A365680, A365682.
%K A365683 nonn,easy,mult
%O A365683 1,2
%A A365683 _Amiram Eldar_, Sep 15 2023