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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..11550

Index entries for sequences related to primorial base

Formula

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

Prog

(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(d<n, v[n/d]*u[d], 0)))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A032742(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];

Crossrefs

Cf. A060681, A276086, A358764, A359428.

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

Cf. also A342417.

Sequence in context: A215269 A352485 A356092 * A336246 A351251 A362988

Adjacent sequences: A359424 A359425 A359426 * A359428 A359429 A359430

Keyword

sign,base

Author

Antti Karttunen, Jan 02 2023

Status

approved