A378749 Dirichlet inverse of A378747, where A378747(n) = A048673(n) - A001065(n).

1, -1, -2, -1, -3, 2, -5, -4, -5, 3, -6, -1, -8, 3, 3, -13, -9, -3, -11, -1, 3, 6, -14, -4, -10, 6, -22, -3, -15, -5, -18, -37, 6, 9, 4, -7, -20, 9, 6, -4, -21, -7, -23, -1, -1, 10, -26, -10, -28, -2, 9, -3, -29, -18, 7, -4, 9, 15, -30, 3, -33, 14, 1, -94, 7, -8, -35, -1, 10, -8, -36, 4, -39, 18, 2, -3, 7, -10, -41

Offset: 1

Author

Antti Karttunen, Dec 09 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.

Crossrefs

Cf. A001065, A048673, A378747.

Cf. also A378750.

Programs

PARI

A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A378747(n) = (A048673(n)-(sigma(n)-n));
memoA378749 = Map();
A378749(n) = if(1==n,1,my(v); if(mapisdefined(memoA378749,n,&v), v, v = -sumdiv(n,d,if(dA378747(n/d)*A378749(d),0)); mapput(memoA378749,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378747(n/d) * a(d).