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

Offset: 1

Author

Antti Karttunen, Nov 14 2017

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A263837, A294888, A294926, A294927, A294929, A294935.

Differs from A032741 for the first time at n=24.

Cf. also A294901.

Programs

Mathematica

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

PARI

A294928(n) = sumdiv(n, d, (d
				

Formula

a(n) = Sum_{d|n, dA294935(d).

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