A323880 Number of divisors d > 1 of n such that A003415(d) divides n, where A003415 gives the arithmetic derivative of n.

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

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..10080

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

a(n) = Sum_{d|n, d>1} [A003415(d)|n], where [ ] is the Iverson bracket, and A003415 gives the arithmetic derivative of n.

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A323880(n) = sumdiv(n, d, (d>1)&&!(n%A003415(d)));

Crossrefs

Cf. A003415.

Cf. also A173441, A323878, A323879.

Sequence in context: A357859 A338731 A081757 * A338651 A033107 A354598

Adjacent sequences: A323877 A323878 A323879 * A323881 A323882 A323883

Keyword

nonn

Author

Antti Karttunen, Feb 07 2019

Status

approved