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Number of divisors d of n for which A003415(d)*d is equal to n, where A003415(x) gives the arithmetic derivative of x.
2

%I #10 Sep 30 2019 03:15:52

%S 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,

%T 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,

%U 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

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

%C Number of times n occurs in A190116.

%H Antti Karttunen, <a href="/A327861/b327861.txt">Table of n, a(n) for n = 1..65537</a>

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

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

%Y Cf. A003415, A190116.

%Y Cf. also A327153, A327166, A327169.

%K nonn

%O 1,4153248

%A _Antti Karttunen_, Sep 28 2019