A378913 a(n) = sum of all positive m such that sigma(m) divides n, where sigma is the sum-of-divisors function (A000203).
1, 1, 3, 4, 1, 8, 5, 11, 3, 1, 1, 28, 10, 18, 11, 11, 1, 35, 1, 23, 7, 1, 1, 87, 1, 10, 3, 33, 1, 45, 42, 63, 3, 1, 5, 77, 1, 38, 30, 57, 1, 112, 1, 47, 11, 1, 1, 202, 5, 1, 3, 13, 1, 122, 1, 107, 52, 1, 1, 205, 1, 103, 39, 63, 10, 8, 1, 71, 3, 18, 1, 389, 1, 74, 11
Offset: 1
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Mathematica
With[{nmax = 100}, Table[Total[PositionIndex[Divisible[n, #[[;; n]]]][True]], {n, nmax}] & [DivisorSigma[1, Range[nmax]]]] -
PARI
a(n) = vecsum(select(x->(!(n % sigma(x))), [1..n])); \\ Michel Marcus, Dec 11 2024