login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A064510 Numbers n such that the sum of the first k divisors of n is equal to n for some k. 9
1, 6, 24, 28, 496, 2016, 8128, 8190, 42336, 45864, 392448, 714240, 1571328, 33550336, 61900800, 91963648, 211891200, 1931236608, 2013143040, 4428914688, 8589869056, 10200236032, 137438691328, 214204956672 (list; graph; refs; listen; history; text; internal format)
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: A219362 A226476 A216793 * A228383 A249667 A114274

Adjacent sequences:  A064507 A064508 A064509 * A064511 A064512 A064513

KEYWORD

nonn,nice,changed

AUTHOR

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

EXTENSIONS

More terms from Don Reble (djr(AT)nk.ca), Dec 17 2001

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

a(24) from Donovan Johnson, Aug 11 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 28 16:04 EDT 2017. Contains 285578 sequences.