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A294928

Number of proper divisors of n that are nonabundant (A263837).

0, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 5, 1, 3, 3, 4, 1, 5, 1, 5, 3, 3, 1, 6, 2, 3, 3, 5, 1, 7, 1, 5, 3, 3, 3, 6, 1, 3, 3, 6, 1, 7, 1, 5, 5, 3, 1, 7, 2, 5, 3, 5, 1, 6, 3, 7, 3, 3, 1, 8, 1, 3, 5, 6, 3, 7, 1, 5, 3, 7, 1, 7, 1, 3, 5, 5, 3, 7, 1, 7, 4, 3, 1, 9, 3, 3, 3, 7, 1, 9, 3, 5, 3, 3, 3, 8, 1, 5, 5, 7, 1, 7, 1, 7, 7

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OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = Sum_{d|n, d<n} A294935(d).

a(n) + A294929(n) = A032741(n).

EXAMPLE

The seven proper divisors of 24 are 1, 2, 3, 4, 6, 8, 12. All except 12 are nonabundant (in A263837), thus a(24) = 6.

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, # < n && DivisorSigma[1, #] <= 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)