A378229 Dirichlet inverse of A341529, where A341529(n) = sigma(n) * A003961(n), and A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

1, -9, -20, 18, -42, 180, -88, 0, 75, 378, -156, -360, -238, 792, 840, 0, -342, -675, -460, -756, 1760, 1404, -696, 0, 245, 2142, 0, -1584, -930, -7560, -1184, 0, 3120, 3078, 3696, 1350, -1558, 4140, 4760, 0, -1806, -15840, -2068, -2808, -3150, 6264, -2544, 0, 847, -2205, 6840, -4284, -3186, 0, 6552, 0, 9200, 8370

Offset: 1

Author

Antti Karttunen, Nov 23 2024

Keywords

• sign
• mult

Comments

Multiplicative because A341529 is.

Links

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

Crossrefs

Dirichlet inverse of A341529.

Cf. also A378228.

Programs

PARI

A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A341529(n) = (sigma(n)*A003961(n));
memoA378229 = Map();
A378229(n) = if(1==n,1,my(v); if(mapisdefined(memoA378229,n,&v), v, v = -sumdiv(n,d,if(dA341529(n/d)*A378229(d),0)); mapput(memoA378229,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA341529(n/d) * a(d).