A364952 Dirichlet inverse of A364557, which is Möbius transform of A005941.

1, -1, -2, -1, -4, 2, -8, -1, 0, 4, -16, 2, -32, 8, 12, -1, -64, 0, -128, 4, 24, 16, -256, 2, 8, 32, 0, 8, -512, -12, -1024, -1, 48, 64, 56, 0, -2048, 128, 96, 4, -4096, -24, -8192, 16, -8, 256, -16384, 2, 48, -8, 192, 32, -32768, 0, 112, 8, 384, 512, -65536, -12, -131072, 1024, -16, -1, 224, -48, -262144, 64, 768

Offset: 1

Author

Antti Karttunen, Aug 29 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000079, A000720, A005941, A364557, A364953.

Cf. also A364574.

Programs

PARI

A364557(n) = if(1==n, 1, 2^(primepi(vecmax(factor(n)[, 1]))+(bigomega(n)-omega(n))-1));
memoA364952 = Map();
A364952(n) = if(1==n,1,my(v); if(mapisdefined(memoA364952,n,&v), v, v = -sumdiv(n,d,if(dA364557(n/d)*A364952(d),0)); mapput(memoA364952,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA364557(n/d) * a(d).

a(p) = -A000079(A000720(p)-1) for all primes p.