A327861 Number of divisors d of n for which A003415(d)*d is equal to n, where A003415(x) gives the arithmetic derivative of x.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0

Offset: 1

Author

Antti Karttunen, Sep 28 2019

Keywords

• nonn

Comments

Number of times n occurs in A190116.

Examples

			a(4153248)=2 as out of 192 divisors of 4153248, only 1368 and 2277 are such that 1368 * A003415(1368) = 2277 * A003415(2277) = 4153248.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A003415, A190116.

Cf. also A327153, A327166, A327169.

Programs

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
A327861(n) = sumdiv(n,d,(d*A003415(d) == n));