%I #4 Jan 06 2024 22:35:55

%S 0,0,2,0,2,0,2,0,10,17,19,17,31,29,31,21,31,20,49,47,49,47,49,27,73,

%T 71,64,71,73,71,73,63,73,71,73,32,109,107,109,99,149,147,149,147,140,

%U 147,149,103,149,147,149,147,149,120,149,139,205,203,205,191,265,263

%N Sum of the refactorable numbers less than n that do not divide n.

%F a(n) = Sum_{k=1..n} k * c(k) * (ceiling(n/k) - floor(n/k)), where c = A336040.

%e a(15) = 31. There are 4 refactorable numbers that are less than 15 that do not divide 15, namely: 2, 8, 9, 12. Their sum is 2 + 8 + 9 + 12 = 31.

%t Table[Sum[k (1 - Ceiling[k/DivisorSigma[0, k]] + Floor[k/DivisorSigma[0, k]]) (Ceiling[n/k] - Floor[n/k]), {k, n}], {n, 100}]

%Y Cf. A033950, A336040, A368572.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Jan 06 2024