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

Author

Paolo P. Lava, Feb 10 2015

Keywords

• nonn

Examples

			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.
		

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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