cp's OEIS Frontend

A351570 Arithmetic derivative of the sum of the divisors of the largest unitary divisor of n that is a square.

%I A351570 #10 Feb 25 2022 17:03:19
%S A351570 0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,
%T A351570 0,20,0,0,0,0,0,0,0,1,1,0,0,1,22,1,0,1,0,0,0,0,0,0,0,1,0,0,1,1,0,0,0,
%U A351570 1,0,0,0,1,0,0,1,1,0,0,0,1,22,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,22,1,38
%N A351570 Arithmetic derivative of the sum of the divisors of the largest unitary divisor of n that is a square.
%C A351570 Observation: There seems to be no terms in range 2..19 in this sequence.
%H A351570 Antti Karttunen, <a href="/A351570/b351570.txt">Table of n, a(n) for n = 1..65537</a>
%H A351570 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A351570 a(n) = A003415(A351568(n)) = A342925(A350388(n)) = A003415(A000203(A350388(n))).
%o A351570 (PARI)
%o A351570 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351570 A350388(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(0==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };
%o A351570 A351570(n) = A003415(sigma(A350388(n)));
%Y A351570 Cf. A000203, A003415, A342925, A350388, A351568, A351571, A351572, A351575 (positions of ones).
%K A351570 nonn
%O A351570 1,36
%A A351570 _Antti Karttunen_, Feb 23 2022