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Sum of the balanced numbers less than n that do not divide n.
1

%I #4 Jan 06 2024 22:58:50

%S 0,0,2,3,5,0,11,9,8,9,11,0,23,21,34,50,52,41,52,50,49,50,52,29,52,50,

%T 49,36,52,26,82,80,79,80,82,94,117,115,114,115,117,92,159,157,141,157,

%U 159,136,159,157,156,157,159,148,159,143,212,213,215,147,215,213,212

%N Sum of the balanced 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 = A351114.

%e a(15) = 34. There are 4 balanced numbers less than 15 that do not divide 15, namely: 2, 6, 12, 14. Their sum is 2 + 6 + 12 + 14 = 34.

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

%Y Cf. A020492, A351114, A368818.

%K nonn,easy

%O 1,3

%A _Wesley Ivan Hurt_, Jan 06 2024