A354866 Dirichlet inverse of A122111.

1, -2, -4, 1, -8, 10, -16, -1, 7, 20, -32, -10, -64, 40, 46, 2, -128, -27, -256, -20, 92, 80, -512, 14, 37, 160, -17, -40, -1024, -150, -2048, -3, 184, 320, 202, 53, -4096, 640, 368, 28, -8192, -300, -16384, -80, -146, 1280, -32768, -26, 175, -129, 736, -160, -65536, 85, 404, 56, 1472, 2560, -131072, 242, -262144

Offset

1,2

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} A122111(n/d) * a(d).

a(n) = A354867(n) - A122111(n).

Prog

(PARI)
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
memoA354866 = Map();
A354866(n) = if(1==n, 1, my(v); if(mapisdefined(memoA354866, n, &v), v, v = -sumdiv(n, d, if(d<n, A122111(n/d)*A354866(d), 0)); mapput(memoA354866, n, v); (v)));

Crossrefs

Cf. A122111, A354867, A354868 (parity), A354869 (positions of odd terms).

Cf. also A354186, A354349, A354351, A354359, A354826.

Sequence in context: A065276 A065288 A065264 * A233034 A204132 A277219

Adjacent sequences: A354863 A354864 A354865 * A354867 A354868 A354869

Keyword

sign

Author

Antti Karttunen, Jun 09 2022

Status

approved