A349359 Sum of A064216 and its Dirichlet inverse, where A064216 = A064989(2n-1), and A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

2, 0, 0, 4, 0, 12, 0, 12, 9, 16, 0, 22, 0, 44, 24, 5, 0, 40, 0, 60, 66, 40, 0, 14, 16, 36, 51, 10, 0, 106, 0, 82, 60, 56, 88, 26, 0, 124, 54, -10, 0, -46, 0, 144, 134, 48, 0, 235, 121, 140, 84, 86, 0, 19, 80, -108, 186, 136, 0, -44, 0, 236, 211, 29, 72, 158, 0, 216, 72, 62, 0, 152, 0, 284, 190, 10, 220, 98, 0, 260, 181

Offset: 1

Author

Antti Karttunen, Nov 17 2021

Keywords

• sign

Comments

Compare to A323894 which in contrast to this sequence seems to have only nonnegative terms.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A064216, A064989, A349358.

Cf. also A323894, A349126.

Programs

PARI

A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A064216(n) = A064989((2*n)-1);
memoA349358 = Map();
A349358(n) = if(1==n,1,my(v); if(mapisdefined(memoA349358,n,&v), v, v = -sumdiv(n,d,if(dA064216(n/d)*A349358(d),0)); mapput(memoA349358,n,v); (v)));
A349359(n) = (A064216(n)+A349358(n));

Formula

a(n) = A064216(n) + A349358(n).

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A064216(d) * A349358(n/d).