A294889 Sum of abundant proper divisors of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 54, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 84, 0, 0, 0, 20, 0, 0, 0, 0, 0

Offset: 1

Author

Antti Karttunen, Nov 14 2017

Keywords

• nonn

Comments

Sum of divisors of n smaller than n that are abundant numbers (in A005101).

Examples

			The proper divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. Of these 12, 20 and 30 are in A005101, thus a(60) = 12+20+30 = 62.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A001065, A005101, A187795, A294929, A294937, A294886, A294887, A294888.

Programs

Mathematica

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

PARI

A294889(n) = sumdiv(n, d, (d(2*d))*d);

Formula

a(n) = Sum_{d|n, dA294937(d)*d.

a(n) = A187795(n) - (A294937(n)*n).

a(n) + A294888(n) = A001065(n).