A359788 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A359788

Dirichlet inverse of A075255, where A075255(n) = n - sopfr(n), where sopfr is the sum of prime factors (with repetition).

1, 0, 0, 0, 0, -1, 0, -2, -3, -3, 0, -5, 0, -5, -7, -8, 0, -10, 0, -11, -11, -9, 0, -15, -15, -11, -18, -17, 0, -20, 0, -22, -19, -15, -23, -25, 0, -17, -23, -29, 0, -30, 0, -29, -34, -21, 0, -33, -35, -38, -31, -35, 0, -37, -39, -43, -35, -27, 0, -42, 0, -29, -50, -48, -47, -50, 0, -47, -43, -56, 0, -38, 0, -35

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

COMMENTS

The first positive term after a(1) occurs as a(144) = 13.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

FORMULA

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A075255(n/d) * a(d).

PROG

(PARI)

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

A075255(n) = (n-A001414(n));

memoA359788 = Map();

A359788(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359788, n, &v), v, v = -sumdiv(n, d, if(d<n, A075255(n/d)*A359788(d), 0)); mapput(memoA359788, n, v); (v)));

CROSSREFS

Cf. A001414, A075255, A359787 (parity of terms).

Cf. also A359789.

Sequence in context: A127572 A021815 A238525 * A075255 A135498 A104172

Adjacent sequences: A359785 A359786 A359787 * A359789 A359790 A359791

KEYWORD

sign

AUTHOR

Antti Karttunen, Jan 15 2023

STATUS

approved