A359823 - OEIS

A359823

Dirichlet inverse of A359820, where A359820 is the characteristic function of numbers whose parity differs from the parity of their arithmetic derivative (A003415).

1, -1, 0, 1, 0, -1, 0, -1, -1, -1, 0, 2, 0, -1, -1, 1, 0, 1, 0, 2, -1, -1, 0, -3, -1, -1, 0, 2, 0, 1, 0, -1, -1, -1, -1, 0, 0, -1, -1, -3, 0, 1, 0, 2, 0, -1, 0, 4, -1, 1, -1, 2, 0, 1, -1, -3, -1, -1, 0, 1, 0, -1, 0, 1, -1, 1, 0, 2, -1, 1, 0, -2, 0, -1, 0, 2, -1, 1, 0, 4, 0, -1, 0, 1, -1, -1, -1, -3, 0, 3, -1, 2, -1, -1, -1, -5, 0

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OFFSET

1,12

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} A359820(n/d) * a(d).

PROG

(PARI)

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A359820(n) = ((n+A003415(n))%2);

memoA359823 = Map();

A359823(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359823, n, &v), v, v = -sumdiv(n, d, if(d<n, A359820(n/d)*A359823(d), 0)); mapput(memoA359823, n, v); (v)));

CROSSREFS

Cf. A000035, A003415, A359820, A359824 (parity of the terms).

Cf. also A359763 [= a(A003961(n))], A359780.

Sequence in context: A364043 A339933 A101659 * A373336 A074272 A328372

Adjacent sequences: A359820 A359821 A359822 * A359824 A359825 A359826

KEYWORD

sign

AUTHOR

Antti Karttunen, Jan 14 2023

STATUS

approved