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

%I #4 Jan 06 2024 22:58:44

%S 0,0,1,1,2,0,3,2,2,2,3,0,4,3,4,5,6,3,6,5,5,5,6,2,6,5,5,4,6,2,7,6,6,6,

%T 7,4,8,7,7,7,8,4,9,8,7,8,9,5,9,8,8,8,9,6,9,7,9,9,10,4,10,9,9,9,10,7,

%U 10,9,9,7,11,7,11,10,9,10,11,8,12,11,11,11,12,6,12

%N Number of balanced numbers less than n that do not divide n.

%F a(n) = Sum_{k=1..n} c(k) * (ceiling(n/k) - floor(n/k)), where c = A351114.

%e a(15) = 4 since there are 4 balanced numbers less than 15 that do not divide 15, namely: 2, 6, 12, 14.

%t Table[Sum[(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, A368819.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Jan 06 2024