A378535 Möbius transform of A378542, where A378542 is the sum of divisors d of n such that n/d has an even number of prime factors (counted with multiplicity).

1, 1, 2, 3, 4, 3, 6, 5, 7, 5, 10, 7, 12, 7, 9, 11, 16, 9, 18, 13, 13, 11, 22, 13, 21, 13, 20, 19, 28, 15, 30, 21, 21, 17, 25, 23, 36, 19, 25, 23, 40, 21, 42, 31, 30, 23, 46, 27, 43, 25, 33, 37, 52, 27, 41, 33, 37, 29, 58, 33, 60, 31, 44, 43, 49, 33, 66, 49, 45, 35, 70, 41, 72, 37, 46, 55, 61, 39, 78, 49, 61, 41, 82

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001222, A008683, A378535, A378536 (Dirichlet inverse).

Programs

PARI

A378542(n) = sumdiv(n,d,d*!(bigomega(n/d)%2));
A378535(n) = sumdiv(n,d,moebius(d)*A378542(n/d));

Formula

a(n) = Sum_{d|n} A008683(d)*A378542(n/d).