A359399 a(1) = 1; a(n) = Sum_{k=2..n} k * a(floor(n/k)).

1, 2, 5, 11, 16, 31, 38, 62, 80, 105, 116, 194, 207, 242, 287, 383, 400, 526, 545, 675, 738, 793, 816, 1200, 1250, 1315, 1423, 1605, 1634, 1979, 2010, 2394, 2493, 2578, 2683, 3475, 3512, 3607, 3724, 4364, 4405, 4888, 4931, 5217, 5577, 5692, 5739, 7563, 7661, 8011

Offset: 1

Author

Seiichi Manyama, Mar 31 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A022825.

Programs

Python

from functools import lru_cache
@lru_cache(maxsize=None)
def A359399(n):
    if n <= 1:
        return 1
    c, j = 0, 2
    k1 = n//j
    while k1 > 1:
        j2 = n//k1 + 1
        c += (j2*(j2-1)-j*(j-1)>>1)*A359399(k1)
        j, k1 = j2, n//j2
    return c+(n*(n+1)-(j-1)*j>>1) # Chai Wah Wu, Mar 31 2023

Formula

G.f. A(x) satisfies A(x) = x + (1/(1 - x)) * Sum_{k>=2} k * (1 - x^k) * A(x^k).