A064510 Numbers n such that the sum of the first k divisors of n is equal to n 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

1,2

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

Links

Table of n, a(n) for n=1..24.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000396, A109883, A109884, A109886, A185584, A194472.

Sequence in context: A216793 A294900 A344700 * A335736 A228383 A249667

Adjacent sequences: A064507 A064508 A064509 * A064511 A064512 A064513

Keyword

nonn,nice

Author

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

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

Status

approved