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A368819
Sum of the balanced numbers less than n that do not divide n.
1
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, 49, 36, 52, 26, 82, 80, 79, 80, 82, 94, 117, 115, 114, 115, 117, 92, 159, 157, 141, 157, 159, 136, 159, 157, 156, 157, 159, 148, 159, 143, 212, 213, 215, 147, 215, 213, 212
OFFSET
1,3
FORMULA
a(n) = Sum_{k=1..n} k * c(k) * (ceiling(n/k) - floor(n/k)), where c = A351114.
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 06 2024
STATUS
approved