A064510 Numbers m such that the sum of the first k divisors of m is equal to m for some k.

1, 6, 24, 28, 496, 2016, 8128, 8190, 42336, 45864, 392448, 714240, 1571328, 33550336, 61900800, 91963648, 211891200, 1931236608, 2013143040, 4428914688, 8589869056, 10200236032, 137438691328, 214204956672

Offset: 1

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 06 2001

Keywords

• nonn
• nice

Comments

Obviously all perfect numbers are included in this sequence.

a(25) > 5*10^11. Other than perfect numbers, 104828758917120, 916858574438400, 967609154764800, 93076753068441600, 215131015678525440 and 1371332329173024768 are also terms. - Donovan Johnson, Dec 26 2012

a(25) > 10^12. - Giovanni Resta, Apr 15 2017

Examples

			Divisors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. 1+2+3+4+6+8 = 24.
		

Crossrefs

Union of A000396 and A194472.

Cf. A109883, A109884, A109886, A185584, A185960, A190940, A307137, A318528, A378313, A378314.

Programs

Mathematica

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 *)
Select[Range[2000000],MemberQ[Accumulate[Divisors[#]],#]&] (* Harvey P. Dale, Mar 22 2012 *)

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

Extensions

More terms from Don Reble, Dec 17 2001

a(19)-a(23) from Donovan Johnson, Aug 31 2008

a(24) from Donovan Johnson, Aug 11 2011