A378451 Dirichlet inverse of A119347, where A119347(n) is the number of distinct sums of distinct divisors of n.

1, -3, -3, 2, -3, 6, -3, 0, 2, 3, -3, 5, -3, 3, 3, 0, -3, -6, -3, 9, 3, 3, -3, -12, 2, 3, 0, -5, -3, 18, -3, 0, 3, 3, 3, 13, -3, 3, 3, 3, -3, -6, -3, -12, -4, 3, -3, 4, 2, -12, 3, -12, -3, -6, 3, 57, 3, 3, -3, -15, -3, 3, -8, 0, 3, -54, -3, -12, 3, -34, -3, -39, -3, 3, -12, -12, 3, -78, -3, -24, 0, 3, -3, 157, 3, 3, 3

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} A119347(n/d) * a(d).

Prog

(PARI)
A119347(n) = { my(c=[0]); fordiv(n, d, c = Set(concat(c, vector(#c, i, c[i]+d)))); (#c)-1; };
memoA378451 = Map();
A378451(n) = if(1==n, 1, my(v); if(mapisdefined(memoA378451, n, &v), v, v = -sumdiv(n, d, if(d<n, A119347(n/d)*A378451(d), 0)); mapput(memoA378451, n, v); (v)));

Crossrefs

Cf. A119347.

Sequence in context: A360206 A003560 A262212 * A123676 A378219 A326814

Adjacent sequences: A378448 A378449 A378450 * A378452 A378453 A378454

Keyword

sign

Author

Antti Karttunen, Nov 29 2024

Status

approved