login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of divisors d > 1 of n such that A003415(d) divides n, where A003415 gives the arithmetic derivative of n.
2

%I #8 Feb 08 2019 00:10:29

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A323880/b323880.txt">Table of n, a(n) for n = 1..10080</a>

%H Antti Karttunen, <a href="/A323880/a323880.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

%o (PARI)

%o 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

%o A323880(n) = sumdiv(n,d,(d>1)&&!(n%A003415(d)));

%Y Cf. A003415.

%Y Cf. also A173441, A323878, A323879.

%K nonn

%O 1,4

%A _Antti Karttunen_, Feb 07 2019