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 A363825 #11 Oct 21 2023 01:50:04
%S A363825 1,2,2,1,2,4,2,3,1,4,2,2,2,4,4,1,2,2,2,2,4,4,2,6,1,4,3,2,2,8,2,3,4,4,
%T A363825 4,1,2,4,4,6,2,8,2,2,2,4,2,2,1,2,4,2,2,6,4,6,4,4,2,4,2,4,2,1,4,8,2,2,
%U A363825 4,8,2,3,2,4,2,2,4,8,2,2,1,4,2,4,4,4,4
%N A363825 The number of infinitary divisors of n that are exponentially odd numbers (A268335).
%C A363825 First differs from A295878 at n = 32.
%H A363825 Amiram Eldar, <a href="/A363825/b363825.txt">Table of n, a(n) for n = 1..10000</a>
%F A363825 Multiplicative with a(p^e) = 1 if e is even, and a(p^e) = 2^A000120(e-1) + 1 if e is odd.
%F A363825 a(n) <= A000005(n) with equality if and only if n is squarefree (A005117).
%t A363825 f[p_, e_] := 1 + If[OddQ[e], 2^DigitCount[e-1, 2, 1], 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A363825 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, 2^hammingweight(f[i, 2]-1) + 1, 1))};
%Y A363825 Cf. A000005, A000120, A005117, A037445, A077609, A268335, A295878, A358260.
%K A363825 nonn,easy,mult
%O A363825 1,2
%A A363825 _Amiram Eldar_, Oct 19 2023