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 A383762 #10 May 11 2025 01:19:38 %S A383762 1,2,2,2,2,4,2,2,2,4,2,4,2,4,4,1,2,4,2,4,4,4,2,4,2,4,2,4,2,8,2,2,4,4, %T A383762 4,4,2,4,4,4,2,8,2,4,4,4,2,2,2,4,4,4,2,4,4,4,4,4,2,8,2,4,4,2,4,8,2,4, %U A383762 4,8,2,4,2,4,4,4,4,8,2,2,1,4,2,8,4,4,4 %N A383762 The number of unitary divisors of n that are exponentially squarefree numbers. %C A383762 First differs from A365499 at n = 32. %C A383762 The sum of these divisors is A383763(n) and the largest of them is A383764(n). %H A383762 Amiram Eldar, <a href="/A383762/b383762.txt">Table of n, a(n) for n = 1..10000</a> %F A383762 Multiplicative with a(p^e) = 2 if e is squarefree (A005117), and 1 otherwise. %F A383762 a(n) <= A034444(n), with equality if and only if n is an exponentially squarefree number (A209061). %F A383762 a(n) <= A365680(n), with equality if and only if n is a squarefree number. %t A383762 f[p_, e_] := If[SquareFreeQ[e], 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A383762 (PARI) a(n) = vecprod(apply(x -> if(issquarefree(x), 2, 1), factor(n)[, 2])); %Y A383762 Cf. A005117, A034444, A077610, A209061, A365499, A365680, A383763, A383764. %K A383762 nonn,easy,mult %O A383762 1,2 %A A383762 _Amiram Eldar_, May 09 2025