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

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, 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, 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

Offset

1,36

Comments

Observation: There seems to be no terms in range 2..19 in this sequence.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

a(n) = A003415(A351568(n)) = A342925(A350388(n)) = A003415(A000203(A350388(n))).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
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); };
A351570(n) = A003415(sigma(A350388(n)));

Crossrefs

Cf. A000203, A003415, A342925, A350388, A351568, A351571, A351572, A351575 (positions of ones).

Sequence in context: A211378 A133591 A137643 * A023921 A072840 A091234

Adjacent sequences: A351567 A351568 A351569 * A351571 A351572 A351573

Keyword

nonn

Author

Antti Karttunen, Feb 23 2022

Status

approved