A365803 Dirichlet inverse of bijective base-3 reverse of n (A263273).

1, -2, -3, 0, -7, 6, -5, 0, 0, 18, -19, 0, -13, -2, 21, 0, -25, 0, -11, -8, 15, 62, -23, 0, 32, 26, 0, 40, -55, -54, -37, -32, 57, 54, -3, 0, -31, -14, 39, 0, -67, 6, -49, -96, 0, 58, -61, 0, -18, -156, 75, 0, -79, 0, 237, -32, 33, 182, -65, 24, -47, 74, 0, 160, 123, -186, -41, 16, 69, 230, -77, 0, -35, 62, -96, 144

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..19683

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A263273(n/d) * a(d).

Prog

(PARI)
A030102(n) = { my(r=[n%3]); while(0<n\=3, r=concat(n%3, r)); subst(Polrev(r), x, 3); };
A263273 = n -> if(!n, n, A030102(n/(3^valuation(n, 3))) * (3^valuation(n, 3)));
memoA365803 = Map();
A365803(n) = if(1==n, 1, my(v); if(mapisdefined(memoA365803, n, &v), v, v = -sumdiv(n, d, if(d<n, A263273(n/d)*A365803(d), 0)); mapput(memoA365803, n, v); (v)));

Crossrefs

Cf. A263273, A323239 (parity of terms), A365804.

Cf. also A365711.

Sequence in context: A350463 A341339 A084257 * A378991 A185963 A059034

Adjacent sequences: A365800 A365801 A365802 * A365804 A365805 A365806

Keyword

sign

Author

Antti Karttunen, Sep 19 2023

Status

approved