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%I #7 May 24 2021 23:31:04
%S 1,2,3,7,8,9,10,11,20,21,22,23,24,25,26,42,43,44,45,46,47,48,49,50,75,
%T 76,77,78,79,80,81,82,83,84,85,121,122,123,124,125,126,127,128,129,
%U 130,131,132,133,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,260
%N a(n) = Sum_{k=1..n} k^c(k), where c(n) is the characteristic function of squares.
%C For 1 <= k <= n, take a running total: add k if k is a perfect square, otherwise add 1. For example, a(12) = 1+1+1+4+1+1+1+1+9+1+1+1 = 23.
%F a(n) = n+m*(m-1)*(2*m+5)/6 where m = floor(sqrt(n)). - _Chai Wah Wu_, May 24 2021
%t Table[Sum[i^(Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]), {i, n}], {n, 80}]
%o (Python 3.8+)
%o from math import isqrt
%o def A344624(n):
%o m = isqrt(n)
%o return n + m*(m-1)*(2*m+5)//6 # _Chai Wah Wu_, May 24 2021
%Y Cf. A010052.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, May 24 2021