A351571 - OEIS

A351571

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

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, 12, 31, 156, 80, 51, 112, 81, 112, 0, 21, 92, 92, 123, 41, 272, 48, 16, 5, 156, 112, 4, 0, 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

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OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

FORMULA

a(n) = A003415(A351569(n)) = A342925(A350389(n)) = A003415(A000203(A350389(n))).

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

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); };