A376414 Dirichlet inverse of sigma(n)-A003415(n), where sigma is the sum of divisors function and A003415 is the arithmetic derivative.

1, -2, -3, 1, -5, 5, -7, 1, 2, 9, -11, -2, -13, 13, 14, 2, -17, -2, -19, -4, 20, 21, -23, -4, 4, 25, 2, -6, -29, -21, -31, 5, 32, 33, 34, 3, -37, 37, 38, -6, -41, -31, -43, -10, -8, 45, -47, -9, 6, -4, 50, -12, -53, -6, 54, -8, 56, 57, -59, 8, -61, 61, -12, 13, 64, -51, -67, -16, 68, -57, -71, 6, -73, 73, -8, -18

Offset: 1

Author

Antti Karttunen, Nov 15 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Dirichlet inverse of A343224.

Cf. A000203, A003415.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A343224(n) = (sigma(n) - A003415(n));
memoA376414 = Map();
A376414(n) = if(1==n,1,my(v); if(mapisdefined(memoA376414,n,&v), v, v = -sumdiv(n,d,if(dA343224(n/d)*A376414(d),0)); mapput(memoA376414,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA343224(n/d) * a(d).