A349358 Dirichlet inverse of A064216, which is A064989(2n-1), where A064989 is fully multiplicative with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

1, -2, -3, -1, -4, 5, -11, 6, -4, -1, -10, 3, -9, 36, 1, -24, -14, 25, -31, 38, 29, -1, -12, -29, -9, 10, 4, -11, -34, 53, -59, 62, 27, -5, 50, -41, -71, 106, 19, -83, -16, -125, -39, 98, 51, -7, -58, 184, 32, 112, -13, -15, -30, -84, -27, -170, 77, 79, -44, -109, -49, 162, 184, -84, -10, 31, -85, 192, -59, -75, -86

Offset: 1

Author

Antti Karttunen, Nov 17 2021

Keywords

• sign

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, A349359, A349398.

Cf. also A323893, A349125.

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)));

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A064216(n/d) * a(d).

a(n) = A349359(n) - A064216(n).