cp's OEIS Frontend

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

%I A323880 #8 Feb 08 2019 00:10:29
%S A323880 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 A323880 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 A323880 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 A323880 Number of divisors d > 1 of n such that A003415(d) divides n, where A003415 gives the arithmetic derivative of n.
%H A323880 Antti Karttunen, <a href="/A323880/b323880.txt">Table of n, a(n) for n = 1..10080</a>
%H A323880 Antti Karttunen, <a href="/A323880/a323880.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A323880 a(n) = Sum_{d|n, d>1} [A003415(d)|n], where [ ] is the Iverson bracket, and A003415 gives the arithmetic derivative of n.
%o A323880 (PARI)
%o A323880 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 A323880(n) = sumdiv(n,d,(d>1)&&!(n%A003415(d)));
%Y A323880 Cf. A003415.
%Y A323880 Cf. also A173441, A323878, A323879.
%K A323880 nonn
%O A323880 1,4
%A A323880 _Antti Karttunen_, Feb 07 2019