A365804 Sum of bijective base-3 reverse of n (A263273) and its Dirichlet inverse.

2, 0, 0, 4, 0, 12, 0, 8, 9, 28, 0, 12, 0, 20, 42, 16, 0, 18, 0, 12, 30, 76, 0, 24, 49, 52, 27, 68, 0, -24, 0, 32, 114, 100, 70, 36, 0, 44, 78, 40, 0, 72, 0, -20, 63, 92, 0, 48, 25, -86, 150, 52, 0, 54, 266, 24, 66, 220, 0, 84, 0, 148, 45, 192, 182, -144, 0, 84, 138, 280, 0, 72, 0, 124, -45, 188, 190, 0, 0, 80, 81

Offset: 1

Author

Antti Karttunen, Sep 19 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A263273, A323239, A365803.

Cf. also A365712.

Programs

PARI

A030102(n) = { my(r=[n%3]); while(0A263273 = 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(dA263273(n/d)*A365803(d),0)); mapput(memoA365803,n,v); (v)));
A365804(n) = (A263273(n)+A365803(n));

Formula

a(n) = A263273(n) + A365803(n).

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1A263273(d) * A365803(n/d).