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 A366902 #13 Apr 22 2025 05:21:28 %S A366902 1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,2,1,1,1,1,3,1,1, %T A366902 1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,4,1,1,1,1, %U A366902 1,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1 %N A366902 The number of exponentially evil divisors of n. %C A366902 First differs from A050361 at n = 128. %C A366902 The number of divisors of n that are exponentially evil numbers (A262675), i.e., numbers having only evil (A001969) exponents in their canonical prime factorization. %C A366902 The sum of these divisors is A366904(n) and the largest of them is A366906(n). %H A366902 Amiram Eldar, <a href="/A366902/b366902.txt">Table of n, a(n) for n = 1..10000</a> %F A366902 Multiplicative with a(p^e) = A159481(e). %F A366902 a(n) >= 1, with equality if and only if n is a cubefree number (A004709). %F A366902 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} Sum_{k>=1} 1/p^A262675(k) = 1.241359937856... . %t A366902 f[p_, e_] := Floor[e/2] + If[OddQ[e] || OddQ[DigitCount[e + 1, 2, 1]], 1, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] %o A366902 (PARI) s(n) = n\2 + (n%2 || hammingweight(n+1)%2); \\ after _Charles R Greathouse IV_ at A159481 %o A366902 a(n) = vecprod(apply(x -> s(x), factor(n)[, 2])); %Y A366902 Cf. A001969, A004709, A050361, A159481, A262675, A366904, A366906. %Y A366902 Similar sequences: A325837, A353898, A365680, A366901. %K A366902 nonn,easy,mult %O A366902 1,8 %A A366902 _Amiram Eldar_, Oct 27 2023