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%I #47 Oct 19 2017 03:13:56
%S 1,6,24,28,496,2016,8128,8190,42336,45864,392448,714240,1571328,
%T 33550336,61900800,91963648,211891200,1931236608,2013143040,
%U 4428914688,8589869056,10200236032,137438691328,214204956672
%N Numbers n such that the sum of the first k divisors of n is equal to n for some k.
%C Obviously all perfect numbers are included in this sequence.
%C a(25) > 5*10^11. Other than perfect numbers, 104828758917120, 916858574438400, 967609154764800, 93076753068441600, 215131015678525440 and 1371332329173024768 are also terms. - _Donovan Johnson_, Dec 26 2012
%C a(25) > 10^12. - _Giovanni Resta_, Apr 15 2017
%e Divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. 1+2+3+4+6+8 = 24.
%t subtract = If[ #1 < #2, Throw[ #1], #1 - #2]&; f[n_] := Catch @ Fold[subtract, n, Divisors @ n]; lst = {}; Do[ If[ f[n] == 0, AppendTo[lst, n]], {n, 10^8}]; lst (* Bobby R. Treat and _Robert G. Wilson v_, Jul 14 2005 *)
%t Select[Range[2000000],MemberQ[Accumulate[Divisors[#]],#]&] (* _Harvey P. Dale_, Mar 22 2012 *)
%o (PARI) isok(n) = {my(d = divisors(n)); my(k = 1); while ((k <= #d) && ((sd = sum(j=1, k, d[j])) != n), k++;); (sd == n);} \\ _Michel Marcus_, Jan 16 2014
%Y Cf. A000396, A109883, A109884, A109886, A185584, A194472.
%K nonn,nice
%O 1,2
%A Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 06 2001
%E More terms from _Don Reble_, Dec 17 2001
%E a(19)-a(23) from _Donovan Johnson_, Aug 31 2008
%E a(24) from _Donovan Johnson_, Aug 11 2011
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