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

1,2

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

Formula

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

Prog

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

Crossrefs

Cf. A009191.

Sequence in context: A157220 A304182 A256284 * A106288 A013633 A334662

Adjacent sequences: A322976 A322977 A322978 * A322980 A322981 A322982

Keyword

nonn

Author

Antti Karttunen, Jan 05 2019

Status

approved