cp's OEIS Frontend

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.

%I A254880 #29 Mar 21 2019 04:38:39
%S A254880 4240,75640,193720,259120,327104,669520,1385480,1613240,2231240,
%T A254880 4185472,12228352,26373640,35095456,37497520,45085240,48211120,
%U A254880 62156512,64754272,81263920,82228432,84099808,109455424,111330208,118899616,118988440,129663880,137013536,139367320
%N 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.
%F A254880 A001065(A294889(a(n))) = a(n).
%e A254880 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.
%p A254880 with(numtheory); P:=proc(q) local a,b,k,n;
%p A254880 for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
%p A254880 for k from 1 to nops(a)-1 do if sigma(a[k])>2*a[k]
%p A254880 then b:=b+a[k]; fi; od; if sigma(b)-b=n
%p A254880 then print(n); fi; od; end: P(10^9);
%t A254880 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 *)
%Y A254880 Cf. A001065, A005101, A254878, A254879, A294889.
%K A254880 nonn
%O A254880 1,1
%A A254880 _Paolo P. Lava_, Feb 10 2015
%E A254880 a(3) inserted and a(11)-a(28) added by _Amiram Eldar_, Mar 20 2019