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 A373968 #13 Mar 30 2025 04:23:18 %S A373968 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,3,0,1,0,1,1,0,0,2,1,0,2,1,0,0,0,4,0,0, %T A373968 1,3,0,0,1,2,0,1,0,1,1,0,0,3,1,2,0,1,0,2,1,2,1,0,0,1,0,0,3,5,1,0,0,1, %U A373968 0,1,0,4,0,0,2,1,1,1,0,3,3,0,0,2,1,0,0,2 %N A373968 a(n) is the number of divisors of n that are Duffinian numbers (A003624). %F A373968 a(p^k) = k - 1, for p prime and k >= 1. %e A373968 Since A003624(1) = 4 then a(1) = a(2) = a(3) = 0 and a(4) = 1. %e A373968 a(8) = 2 because 8 has the divisors 4 = A003624(1) and 8 = A003624(2). %t A373968 a[n_] := DivisorSum[n, 1 &, CompositeQ[#] && CoprimeQ[#, DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, Jul 19 2024 *) %o A373968 (Magma) f:=func<n|n ne 1 and not IsPrime(n) and Gcd(n,DivisorSigma(1,n)) eq 1>; [#[d:d in Divisors(k)|f(d)]:k in [1..100]]; %Y A373968 Cf. A000203, A003624, A009194. %K A373968 nonn %O A373968 1,8 %A A373968 _Marius A. Burtea_, Jul 12 2024