cp's OEIS Frontend

A351571 Arithmetic derivative of the sum of the divisors of the largest unitary divisor of n that is an exponentially odd number.

%I A351571 #9 Feb 25 2022 17:03:25
%S A351571 0,1,4,0,5,16,12,8,0,21,16,4,9,44,44,0,21,1,24,5,80,60,44,92,0,41,68,
%T A351571 12,31,156,80,51,112,81,112,0,21,92,92,123,41,272,48,16,5,156,112,4,0,
%U A351571 1,156,9,81,244,156,244,176,123,92,44,33,272,12,0,124,384,72,21,272,384,156,8,39,101,4,24,272,332,176,5
%N A351571 Arithmetic derivative of the sum of the divisors of the largest unitary divisor of n that is an exponentially odd number.
%H A351571 Antti Karttunen, <a href="/A351571/b351571.txt">Table of n, a(n) for n = 1..20000</a>
%H A351571 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A351571 a(n) = A003415(A351569(n)) = A342925(A350389(n)) = A003415(A000203(A350389(n))).
%o A351571 (PARI)
%o A351571 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A351571 A350389(n) = { my(m=1, f=factor(n)); for(k=1,#f~,if(1==(f[k,2]%2), m *= (f[k,1]^f[k,2]))); (m); };
%o A351571 A351571(n) = A003415(sigma(A350389(n)));
%Y A351571 Cf. A000203, A003415, A268335 (exponentially odd numbers), A342925, A350389, A351569, A351570, A351573.
%K A351571 nonn,look
%O A351571 1,3
%A A351571 _Antti Karttunen_, Feb 23 2022