A320225 a(1) = 1; a(n > 1) = Sum_{k = 1..n} Sum_{d|k, d < k} a(d).

1, 1, 2, 4, 5, 9, 10, 16, 19, 26, 27, 44, 45, 57, 65, 87, 88, 120, 121, 158, 171, 200, 201, 278, 284, 331, 353, 426, 427, 536, 537, 646, 676, 766, 782, 982, 983, 1106, 1154, 1365, 1366, 1617, 1618, 1851, 1943, 2146, 2147, 2589, 2600, 2917, 3008, 3390, 3391

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; a(n > 1) = Sum_{d = 1..n-1} a(d) * floor(n/d-1).

G.f. A(x) satisfies A(x) = x + (1/(1 - x)) * Sum_{k>=2} A(x^k). - Ilya Gutkovskiy, Sep 06 2019

Mathematica

sau[n_]:=If[n==1, 1, Sum[sau[d], {k, n}, {d, Most[Divisors[k]]}]];
Table[sau[n], {n, 30}]

Prog

(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
def A320225(n): return 1 if n == 1 else sum(A320225(d)*(n//d-1) for d in range(1, n)) # Chai Wah Wu, Jun 08 2022

Crossrefs

Cf. A002541, A003238, A010766, A014668, A126656, A167865, A316782, A317712, A320222, A320224.

Sequence in context: A363283 A213011 A175265 * A070924 A351993 A266197

Adjacent sequences: A320222 A320223 A320224 * A320226 A320227 A320228

Keyword

nonn

Author

Gus Wiseman, Oct 07 2018

Status

approved