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