A322979 a(n) = Sum A009191(d) over the divisors d of n, where A009191(x) = gcd(x, A000005(x)), and A000005(x) gives the number of divisors of x.

1, 3, 2, 4, 2, 6, 2, 8, 5, 6, 2, 13, 2, 6, 4, 9, 2, 15, 2, 9, 4, 6, 2, 25, 3, 6, 6, 9, 2, 12, 2, 11, 4, 6, 4, 31, 2, 6, 4, 21, 2, 12, 2, 9, 10, 6, 2, 28, 3, 9, 4, 9, 2, 18, 4, 21, 4, 6, 2, 33, 2, 6, 10, 12, 4, 12, 2, 9, 4, 12, 2, 55, 2, 6, 8, 9, 4, 12, 2, 32, 7, 6, 2, 33, 4, 6, 4, 21, 2, 30, 4, 9, 4, 6, 4, 42, 2, 9, 10, 13, 2, 12, 2, 21, 8

Offset: 1

Author

Antti Karttunen, Jan 05 2019

Keywords

• nonn

Comments

Inverse Möbius transform of A009191.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10080
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A009191.

Programs

PARI

A009191(n) = gcd(n, numdiv(n));
A322979(n) = sumdiv(n,d,A009191(d));

Formula

a(n) = Sum_{d|n} A009191(d).