A354867 Sum of A122111 and its Dirichlet inverse.

2, 0, 0, 4, 0, 16, 0, 4, 16, 32, 0, 0, 0, 64, 64, 9, 0, -12, 0, 0, 128, 128, 0, 28, 64, 256, 8, 0, 0, -120, 0, 8, 256, 512, 256, 74, 0, 1024, 512, 56, 0, -240, 0, 0, -96, 2048, 0, -4, 256, -84, 1024, 0, 0, 120, 512, 112, 2048, 4096, 0, 284, 0, 8192, -192, 20, 1024, -480, 0, 0, 4096, -552, 0, -64, 0, 16384, -264, 0, 1024

Offset: 1

Author

Antti Karttunen, Jun 09 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A122111, A354866.

Cf. also A354352.

Programs

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(dA122111(n/d)*A354866(d),0)); mapput(memoA354866,n,v); (v)));
A354867(n) = (A122111(n)+A354866(n));

Formula

a(n) = A122111(n) + A354866(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A122111(d) * A354866(n/d).