A359789 Dirichlet inverse of A036288, where A036288(n) = 1 + sopfr(n), where sopfr is the sum of prime divisors with repetition, A001414.

1, -3, -4, 4, -6, 18, -8, -4, 9, 28, -12, -40, -14, 38, 39, 4, -18, -63, -20, -64, 53, 58, -24, 64, 25, 68, -18, -88, -30, -253, -32, -4, 81, 88, 83, 216, -38, 98, 95, 104, -42, -347, -44, -136, -144, 118, -48, -88, 49, -175, 123, -160, -54, 180, 127, 144, 137, 148, -60, 820, -62, 158, -198, 4, 149, -535

Offset: 1

Author

Antti Karttunen, Jan 15 2023

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A001414, A036288, A359774 (parity of terms).

Cf. also A359773, A359788, A359790, A359791.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
memoA359789 = Map();
A359789(n) = if(1==n,1,my(v); if(mapisdefined(memoA359789,n,&v), v, v = -sumdiv(n,d,if(dA001414(n/d))*A359789(d),0)); mapput(memoA359789,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA036288(n/d) * a(d).