cp's OEIS Frontend

A347028 a(1) = 1; a(n+1) = -Sum_{k=1..n} a(floor(n/k)).

%I A347028 #8 Apr 29 2025 21:14:06
%S A347028 1,-1,0,-2,1,-3,1,-4,4,-6,2,-7,8,-8,5,-13,13,-14,9,-15,19,-21,12,-22,
%T A347028 32,-26,18,-36,33,-37,31,-38,57,-48,32,-56,66,-57,44,-74,83,-75,65,
%U A347028 -76,100,-102,68,-103,140,-108,94,-136,140,-137,119,-149,193,-174,125,-175,228,-176,161,-224,256
%N A347028 a(1) = 1; a(n+1) = -Sum_{k=1..n} a(floor(n/k)).
%F A347028 G.f. A(x) satisfies: A(x) = x - (x/(1 - x)) * Sum_{k>=1} (1 - x^k) * A(x^k).
%t A347028 a[1] = 1; a[n_] := a[n] = -Sum[a[Floor[(n - 1)/k]], {k, 1, n - 1}]; Table[a[n], {n, 1, 65}]
%t A347028 nmax = 65; A[_] = 0; Do[A[x_] = x - (x/(1 - x)) Sum[(1 - x^k) A[x^k], {k, 1, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest
%o A347028 (Python)
%o A347028 from functools import lru_cache
%o A347028 @lru_cache(maxsize=None)
%o A347028 def A347028(n):
%o A347028     if n == 1:
%o A347028         return 1
%o A347028     c, j, k1 = n, 1, n-1
%o A347028     while k1 > 1:
%o A347028         j2 = (n-1)//k1 + 1
%o A347028         c += (j2-j)*A347028(k1)
%o A347028         j, k1 = j2, (n-1)//j2
%o A347028     return j-c # _Chai Wah Wu_, Apr 29 2025
%Y A347028 Cf. A078346, A309288, A328967.
%K A347028 sign
%O A347028 1,4
%A A347028 _Ilya Gutkovskiy_, Aug 11 2021