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

1,1

Links

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

Formula

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

a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A263273(d) * A365803(n/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)));
A365804(n) = (A263273(n)+A365803(n));

Crossrefs

Cf. A263273, A323239, A365803.

Cf. also A365712.

Sequence in context: A323884 A061669 A324641 * A349359 A323894 A349383

Adjacent sequences: A365801 A365802 A365803 * A365805 A365806 A365807

Keyword

sign

Author

Antti Karttunen, Sep 19 2023

Status

approved