A355003 a(n) = gcd(A003415(n), A277791(n)), where A003415 is the arithmetic derivative and A277791 is the denominator of sum of reciprocals of proper divisors of n.

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 4, 1, 1, 1, 8, 1, 3, 1, 4, 1, 1, 1, 4, 5, 1, 9, 4, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 3, 1, 1, 16, 7, 5, 1, 4, 1, 27, 1, 4, 1, 1, 1, 4, 1, 1, 3, 32, 1, 1, 1, 4, 1, 1, 1, 12, 1, 1, 5, 4, 1, 1, 1, 16, 27, 1, 1, 4, 1, 1, 1, 4, 1, 3, 1, 4, 1, 1, 1, 16, 1, 7, 3, 5, 1, 1, 1, 4, 1

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A277791.

Cf. also A355815.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A277791(n) = denominator((sigma(n)-1)/n); \\ From A277791
A355003(n) = gcd(A003415(n), A277791(n));

Formula

a(n) = gcd(A003415(n), A277791(n)).

a(p^k) = p^(k-1) for all primes p and exponents k > 0.