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

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A364557(n/d) * a(d).

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

Prog

(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(d<n, A364557(n/d)*A364952(d), 0)); mapput(memoA364952, n, v); (v)));

Crossrefs

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

Cf. also A364574.

Sequence in context: A079966 A101707 A304587 * A113418 A117000 A082392

Adjacent sequences: A364949 A364950 A364951 * A364953 A364954 A364955

Keyword

sign

Author

Antti Karttunen, Aug 29 2023

Status

approved