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

Offset: 1

Author

Antti Karttunen, Feb 23 2022

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003415, A268335 (exponentially odd numbers), A342925, A350389, A351569, A351570, A351573.

Programs

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); };
A351571(n) = A003415(sigma(A350389(n)));

Formula

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