A337345 Number of divisors d of n for which A003961(d) > 2*d, where A003961 is fully multiplicative with a(p) = nextprime(p).

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 3, 1, 0, 0, 5, 0, 0, 2, 3, 0, 4, 0, 4, 0, 0, 1, 6, 0, 0, 1, 5, 0, 4, 0, 2, 3, 0, 0, 7, 1, 2, 0, 2, 0, 5, 0, 5, 1, 0, 0, 8, 0, 0, 3, 5, 0, 2, 0, 2, 1, 4, 0, 9, 0, 0, 2, 2, 0, 3, 0, 7, 3, 0, 0, 8, 0, 0, 0, 4, 0, 8, 1, 2, 0, 0, 0, 9, 0, 3, 2, 5, 0, 2, 0, 4, 4

Offset: 1

Author

Antti Karttunen, Aug 27 2020

Keywords

• nonn

Comments

Number of terms of A246282 that divide n.

Number of divisors d of n for which A048673(d) > d.

Links

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

Crossrefs

Inverse Möbius transform of A252742.

Cf. A003961, A048673, A246282, A337346, A337372 (positions of ones), A341609 (their characteristic function), A341610 (positions of terms > 1), A378658 [= a(A091191(n))], A378662, A378663.

Cf. also A080224, A337541, A341620.

Programs

PARI

A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A337345(n) = sumdiv(n,d,A003961(d)>(d+d));

Formula

a(n) = Sum_{d|n} A252742(d).

a(n) = A337346(n) + A252742(n).

From Antti Karttunen, Dec 10 2024: (Start)

a(n) = 1 <=> A341609(n) = 1.

a(n) = A378662(n) + A080224(n) = A378663(n) + A341620(n).

(End)