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A368818
Number of balanced numbers less than n that do not divide n.
1
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, 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, 10, 9, 9, 7, 11, 7, 11, 10, 9, 10, 11, 8, 12, 11, 11, 11, 12, 6, 12
OFFSET
1,5
FORMULA
a(n) = Sum_{k=1..n} c(k) * (ceiling(n/k) - floor(n/k)), where c = A351114.
EXAMPLE
a(15) = 4 since there are 4 balanced numbers less than 15 that do not divide 15, namely: 2, 6, 12, 14.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 06 2024
STATUS
approved