A337541 Number of divisors d of n for which sigma(A003961(d)) >= 2*sigma(d), where sigma is the sum of divisors, and A003961(x) shifts the prime factorization of x one step towards larger primes.

0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 2, 0, 3, 0, 1, 1, 0, 0, 4, 0, 0, 2, 2, 0, 3, 0, 3, 0, 0, 1, 5, 0, 0, 0, 3, 0, 4, 0, 1, 3, 0, 0, 6, 1, 1, 0, 1, 0, 5, 0, 4, 0, 0, 0, 6, 0, 0, 3, 4, 0, 2, 0, 1, 0, 3, 0, 8, 0, 0, 2, 1, 0, 2, 0, 5, 3, 0, 0, 7, 0, 0, 0, 3, 0, 7, 0, 1, 0, 0, 0, 8, 0, 3, 2, 3, 0, 2, 0, 3, 4

Offset: 1

Author

Antti Karttunen, Aug 31 2020

Keywords

• nonn

Comments

Number of terms of A337381 that divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Inverse Möbius transform of A337383.

Cf. A000203, A003961, A003973, A337381, A337542, A337543 (positions of ones).

Cf. also A337345.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337541(n) = sumdiv(n,d,sigma(A003961(d))>=2*sigma(d));

Formula

a(n) = Sum_{d|n} A337383(d).

a(n) = A337542(n) + A337383(n).