A254880 Let 's' denote the sum of the abundant numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s)-s is equal to x.

4240, 75640, 193720, 259120, 327104, 669520, 1385480, 1613240, 2231240, 4185472, 12228352, 26373640, 35095456, 37497520, 45085240, 48211120, 62156512, 64754272, 81263920, 82228432, 84099808, 109455424, 111330208, 118899616, 118988440, 129663880, 137013536, 139367320

Offset

1,1

Links

Table of n, a(n) for n=1..28.

Formula

A001065(A294889(a(n))) = a(n).

Example

Aliquot divisors of 4240 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 53, 80, 106, 212, 265, 424, 530, 848, 1060, 2120 and the abundant numbers are 20, 40, 80, 1060, 2120. Their sum is 3320 and sigma(3320) - 3320 = 4240.

Maple

with(numtheory); P:=proc(q) local a, b, k, n;
for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
for k from 1 to nops(a)-1 do if sigma(a[k])>2*a[k]
then b:=b+a[k]; fi; od; if sigma(b)-b=n
then print(n); fi; od; end: P(10^9);

Mathematica

seqQ[n_] := Module[{s = Total@Select[Most[Divisors[n]], DivisorSigma[1, #] > 2# &]}, s>0 && DivisorSigma[1, s] - s == n]; Select[Range[10^6], seqQ] (* Amiram Eldar, Mar 20 2019 *)

Crossrefs

Cf. A001065, A005101, A254878, A254879, A294889.

Sequence in context: A035899 A035783 A108007 * A184684 A204872 A204638

Adjacent sequences: A254877 A254878 A254879 * A254881 A254882 A254883

Keyword

nonn

Author

Paolo P. Lava, Feb 10 2015

Extensions

a(3) inserted and a(11)-a(28) added by Amiram Eldar, Mar 20 2019

Status

approved