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

1,12

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)

Formula

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

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

Prog

(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));

Crossrefs

Inverse Möbius transform of A337383.

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

Cf. also A337345.

Sequence in context: A202177 A354793 A029360 * A185279 A088432 A329747

Adjacent sequences: A337538 A337539 A337540 * A337542 A337543 A337544

Keyword

nonn

Author

Antti Karttunen, Aug 31 2020

Status

approved