A359427 Dirichlet inverse of A358764.

1, -2, -3, -2, -9, 8, -5, 6, -6, 6, -45, -4, -25, -30, -21, -130, -225, -70, -125, -130, -345, -570, -1125, -480, -544, -1150, -1812, -3550, -5625, 222, -7, 530, 249, 858, 27, 418, -35, 430, 45, 610, -315, 1520, -175, 2650, -48, 3450, -1575, 2060, -850, 804, -1275, -250, -7875, 4288, -3565, 6150, -12375

Offset: 1

Author

Antti Karttunen, Jan 02 2023

Keywords

• sign
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A060681, A276086, A358764, A359428.

Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.

Cf. also A342417.

Programs

PARI

up_to = 11550;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A060681(n) = (n-A032742(n));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A358764(n) = A060681(A276086(n));
v359427 = DirInverseCorrect(vector(up_to,n,A358764(n)));
A359427(n) = v359427[n];

Formula

a(n) = A359428(n) - A358764(n).