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

%I A359399 #16 Apr 01 2023 11:23:52
%S A359399 1,2,5,11,16,31,38,62,80,105,116,194,207,242,287,383,400,526,545,675,
%T A359399 738,793,816,1200,1250,1315,1423,1605,1634,1979,2010,2394,2493,2578,
%U A359399 2683,3475,3512,3607,3724,4364,4405,4888,4931,5217,5577,5692,5739,7563,7661,8011
%N A359399 a(1) = 1; a(n) = Sum_{k=2..n} k * a(floor(n/k)).
%H A359399 Seiichi Manyama, <a href="/A359399/b359399.txt">Table of n, a(n) for n = 1..10000</a>
%F A359399 G.f. A(x) satisfies A(x) = x + (1/(1 - x)) * Sum_{k>=2} k * (1 - x^k) * A(x^k).
%o A359399 (Python)
%o A359399 from functools import lru_cache
%o A359399 @lru_cache(maxsize=None)
%o A359399 def A359399(n):
%o A359399     if n <= 1:
%o A359399         return 1
%o A359399     c, j = 0, 2
%o A359399     k1 = n//j
%o A359399     while k1 > 1:
%o A359399         j2 = n//k1 + 1
%o A359399         c += (j2*(j2-1)-j*(j-1)>>1)*A359399(k1)
%o A359399         j, k1 = j2, n//j2
%o A359399     return c+(n*(n+1)-(j-1)*j>>1) # _Chai Wah Wu_, Mar 31 2023
%Y A359399 Cf. A022825.
%K A359399 nonn
%O A359399 1,2
%A A359399 _Seiichi Manyama_, Mar 31 2023