A359602 Sum of A244042 and its Dirichlet inverse, where A244042(n) replaces 2's with 0's in the ternary representation of n.

2, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 24, 0, 0, 18, 16, 0, 0, 0, 24, 6, 0, 0, 0, 9, 0, 27, 8, 0, 60, 0, 0, 54, 0, 6, 36, 0, 0, 78, 80, 0, 72, 0, 72, 27, 0, 0, 12, 1, 60, 54, 104, 0, 0, 54, 96, 6, 0, 0, -72, 0, 0, 9, 16, 78, 24, 0, 72, 18, 92, 0, 0, 0, 0, -21, 8, 18, 0, 0, -84, 81, 0, 0, 144, 54, 0, 162, 32

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..19682

Formula

a(n) = A244042(n) + A359601(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A244042(d) * A359601(n/d).

Prog

(PARI)
A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
memoA359601 = Map();
A359601(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359601, n, &v), v, v = -sumdiv(n, d, if(d<n, A244042(n/d)*A359601(d), 0)); mapput(memoA359601, n, v); (v)));
A359602(n) = (A244042(n)+A359601(n));

Crossrefs

Cf. A244042, A359601.

Cf. A053850 (positions of odd terms), A353569 (parity of terms).

Sequence in context: A282530 A060478 A088806 * A280618 A347714 A089807

Adjacent sequences: A359599 A359600 A359601 * A359603 A359604 A359605

Keyword

sign,base,easy

Author

Antti Karttunen, Jan 11 2023

Status

approved