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

1,24

Comments

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

Links

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

Index entries for sequences related to sums of divisors.

Formula

a(n) = Sum_{d|n, d<n} A294937(d)*d.

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

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

Example

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.

Mathematica

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

Prog

(PARI) A294889(n) = sumdiv(n, d, (d<n)*(sigma(d)>(2*d))*d);

Crossrefs

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

Sequence in context: A257304 A241570 A083344 * A308425 A063863 A236238

Adjacent sequences: A294886 A294887 A294888 * A294890 A294891 A294892

Keyword

nonn

Author

Antti Karttunen, Nov 14 2017

Status

approved