A378536 Inverse Möbius transform of A378525.

1, -1, -2, -2, -4, 1, -6, 0, -3, 3, -10, 5, -12, 5, 7, 0, -16, 5, -18, 9, 11, 9, -22, 2, -5, 11, 0, 13, -28, -1, -30, 0, 19, 15, 23, 5, -36, 17, 23, 2, -40, -3, -42, 21, 14, 21, -46, 0, -7, 9, 31, 25, -52, 3, 39, 2, 35, 27, -58, -18, -60, 29, 20, 0, 47, -7, -66, 33, 43, -13, -70, -5, -72, 35, 14, 37, 59, -9, -78, 0, 0

Offset: 1

Author

Antti Karttunen, Dec 01 2024

Keywords

• sign

Comments

Dirichlet inverse of A378535, which is 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).

Links

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

Crossrefs

Cf. A378525, A378535 (Dirichlet inverse), A378542.

Programs

PARI

memoA378525 = Map();
A378525(n) = if(1==n,1,my(v); if(mapisdefined(memoA378525,n,&v), v, v = -sumdiv(n,d,if(dA378542(n/d)*A378525(d),0)); mapput(memoA378525,n,v); (v)));
A378536(n) = sumdiv(n,d,A378525(d));

Formula

a(n) = Sum_{d|n} A378525(d).