A378663 Number of divisors d of n such that sigma(d) < 2*d < A003961(d), where A003961 is fully multiplicative with a(p) = nextprime(p).

0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 3, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 1, 2, 0, 0, 1, 3, 0, 2, 0, 2, 3, 0, 0, 3, 1, 2, 0, 2, 0, 2, 0, 3, 1, 0, 0, 3, 0, 0, 3, 5, 0, 0, 0, 2, 1, 3, 0, 3, 0, 0, 2, 2, 0, 1, 0, 4, 3, 0, 0, 3, 0, 0, 0, 3, 0, 4, 1, 2, 0, 0, 0, 4, 0, 3, 2, 3, 0, 0, 0, 3, 4

Offset: 1

Author

Antti Karttunen, Dec 06 2024

Keywords

• nonn

Comments

Number of terms of A341615 that divide n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to prime indices in the factorization of n
• Index entries for sequences related to sigma(n)

Crossrefs

Inverse Möbius transform of A341613.

Cf. A000203, A003961, A080225, A337345, A341615, A341620, A378662.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A341613(n) = ((sigma(n)<(2*n))&&((2*n)<A003961(n)));
A378663(n) = sumdiv(n,d,A341613(d));

Formula

a(n) = Sum_{d|n} A341613(d).

a(n) = A337345(n) - A341620(n).

a(n) = A378662(n) - A080225(n).