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 A377381 #9 Dec 21 2024 01:03:20 %S A377381 0,0,0,1,0,1,0,1,1,0,0,3,0,0,1,1,0,3,0,1,1,0,0,3,0,1,1,1,0,3,0,1,0,1, %T A377381 0,5,0,0,1,1,0,3,0,1,3,0,0,3,0,1,0,2,0,3,0,2,0,0,0,6,0,0,2,2,0,1,0,2, %U A377381 1,0,0,6,0,0,1,2,0,3,0,1,2,0,0,5,0,1,0 %N A377381 a(n) is the number of divisors of n that are interprime numbers (A024675). %e A377381 Because A024675(1) = 4 it follows that a(1) = a(2) = a(3) = 0 and a(4) = 1. %e A377381 a(12) = 3 because it has the divisors 4 = A024675(1), 6 = A024675(2) and 12 = A024675(4). %t A377381 a[n_] := DivisorSum[n, 1 &, CompositeQ[#] && NextPrime[#] + NextPrime[#, -1] == 2*# &]; Array[a, 100] (* _Amiram Eldar_, Dec 11 2024 *) %o A377381 (Magma) ipr:=func<n|n ge 3 and not IsPrime(n) and 2*n eq NextPrime(n)+PreviousPrime(n)> ;[#[d:d in Divisors(n)|ipr(d)]:n in [1..100]]; %Y A377381 Cf. A024675. %K A377381 nonn %O A377381 1,12 %A A377381 _Marius A. Burtea_, Dec 05 2024