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A078346 a(1) = 1; a(n) = Sum_{k=1..n-1} a(floor((n-1)/k)).

%I A078346 #20 Aug 03 2025 02:20:51
%S A078346 1,1,2,4,7,11,17,24,34,46,62,79,104,130,163,201,249,298,363,429,513,
%T A078346 605,714,824,966,1112,1284,1468,1687,1907,2181,2456,2779,3120,3510,
%U A078346 3910,4394,4879,5430,6008,6677,7347,8139,8932,9836,10788,11850,12913
%N A078346 a(1) = 1; a(n) = Sum_{k=1..n-1} a(floor((n-1)/k)).
%F A078346 For k>1, a(prime(k)+1)=2*a(prime(k))-a(prime(k)-1)+1. - _Benoit Cloitre_, Aug 29 2004
%F A078346 G.f. A(x) satisfies: A(x) = x + (x/(1 - x)) * Sum_{k>=1} (1 - x^k) * A(x^k). - _Ilya Gutkovskiy_, Aug 11 2021
%o A078346 (Python)
%o A078346 from functools import lru_cache
%o A078346 @lru_cache(maxsize=None)
%o A078346 def A078346(n):
%o A078346     if n == 1:
%o A078346         return 1
%o A078346     c, j, k1 = n, 1, n-1
%o A078346     while k1 > 1:
%o A078346         j2 = (n-1)//k1 + 1
%o A078346         c += (j2-j)*A078346(k1)
%o A078346         j, k1 = j2, (n-1)//j2
%o A078346     return c-j # _Chai Wah Wu_, Apr 29 2025
%Y A078346 Partial sums of A320224.
%K A078346 nonn
%O A078346 1,3
%A A078346 _Benoit Cloitre_, Nov 22 2002