A378523 Dirichlet inverse of A332993, where A332993 is defined as a(1) = 1, and for n > 1, a(n) = n + a(A032742(n)), and A032742 is the largest proper divisor.

1, -3, -4, 2, -6, 14, -8, 0, 3, 20, -12, -14, -14, 26, 27, 0, -18, -17, -20, -18, 35, 38, -24, 4, 5, 44, 0, -22, -30, -109, -32, 0, 51, 56, 53, 34, -38, 62, 59, 4, -42, -137, -44, -30, -30, 74, -48, 0, 7, -27, 75, -34, -54, 6, 77, 4, 83, 92, -60, 146, -62, 98, -36, 0, 89, -193, -68, -42, 99, -199, -72, -28, -74, 116

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A332993(n/d) * a(d).

Prog

(PARI)
A332993(n) = if(1==n, n, n + A332993(n/vecmin(factor(n)[, 1])));
memoA378523 = Map();
A378523(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378523, n, &v), v, v = -sumdiv(n, d, if(d<n, A332993(n/d)*A378523(d), 0)); mapput(memoA378523, n, v); (v)));

Crossrefs

Cf. A032742, A332993.

Cf. also A378524.

Sequence in context: A344968 A324340 A046692 * A205769 A166108 A255768

Adjacent sequences: A378520 A378521 A378522 * A378524 A378525 A378526

Keyword

sign,new

Author

Antti Karttunen, Nov 30 2024

Status

approved