A337542 Number of proper 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, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 3, 0, 0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 3, 0, 0, 0, 5, 0, 0, 2, 3, 0, 1, 0, 0, 0, 2, 0, 7, 0, 0, 1, 0, 0, 1, 0, 4, 2, 0, 0, 6, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 7, 0, 2, 1, 2, 0, 1, 0, 2, 3

Offset

1,18

Comments

Number of terms of A337381 less than n 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, d<n} A337383(d).

a(n) = A337541(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); };
A337542(n) = sumdiv(n, d, (d<n)&&sigma(A003961(d))>=2*sigma(d));

Crossrefs

Cf. A000203, A003961, A337381, A337383, A337541, A337543.

Cf. also A337346.

Sequence in context: A047764 A022883 A284270 * A282568 A028833 A024943

Adjacent sequences: A337539 A337540 A337541 * A337543 A337544 A337545

Keyword

nonn

Author

Antti Karttunen, Aug 31 2020

Status

approved