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 A383764 #9 May 11 2025 01:18:41
%S A383764 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,1,17,18,19,20,21,22,23,24,25,26,
%T A383764 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,3,49,
%U A383764 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68
%N A383764 The largest unitary divisor of n that is an exponentially squarefree number.
%C A383764 First differs from A053165 at n = 32.
%C A383764 The number of these divisors is A383762(n) and their sum is A383763(n).
%H A383764 Amiram Eldar, <a href="/A383764/b383764.txt">Table of n, a(n) for n = 1..10000</a>
%F A383764 Multiplicative with a(p^e) = p^e if e is squarefree (A005117), and 1 otherwise.
%F A383764 a(n) <= A365683(n), with equality if and only if n is an exponentially squarefree number (A209061).
%F A383764 a(n) <= n, with equality if and only if n is an exponentially squarefree number.
%t A383764 f[p_, e_] := If[SquareFreeQ[e], p^e, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A383764 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(issquarefree(f[i,2]), f[i,1]^f[i,2], 1));}
%Y A383764 Cf. A005117, A053165, A077610, A209061, A365683, A383762, A383763.
%K A383764 nonn,easy,mult
%O A383764 1,2
%A A383764 _Amiram Eldar_, May 09 2025