A056550 Numbers k such that Sum_{j=1..k} sigma(j) is divisible by k, where sigma(j) = sum of divisors of j (A000203).

1, 2, 8, 11, 17, 63, 180, 259, 818, 2161, 4441, 8305, 11998, 694218, 3447076, 4393603, 57402883, 73459800, 121475393, 2068420025, 5577330586, 13320495021, 35297649260, 138630178659, 988671518737

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

Values of k for which A024916(k)/k is integer.

Also values of k for which A004125(k)/k is integer. [Paolo P. Lava, Jan 08 2013]

Example

a(3) = 8 is in the sequence because A024916(8) / 8 = 56 / 8 = 7 is an integer. [Jaroslav Krizek, Dec 07 2009]

Maple

f := []: for i from 1 to 9000 do if add(sigma(n), n=1..i) mod i = 0 then f := [op(f), i] fi; od; f;

Mathematica

k=10^4; a[1]=1; a[n_]:=a[n]=DivisorSigma[1, n]+a[n-1]; s=a/@Range@k; Select[Range@k, Divisible[s[[#]], #]&] (* Ivan N. Ianakiev, Apr 30 2016 *)
Module[{nn=44*10^5, ds}, ds=Accumulate[DivisorSigma[1, Range[nn]]]; Select[ Thread[{ds, Range[nn]}], Divisible[#[[1]], #[[2]]]&]][[All, 2]] (* The program generates the first 16 terms of the sequence. To generate more, increase the value of nn. *) (* Harvey P. Dale, Dec 04 2018 *)

Prog

(PARI) is(n)=sum(k=1, n, n\k*k)%n==0 \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A000203, A024916, A168133, A168132.

Sequence in context: A129516 A220269 A143189 * A074263 A295070 A009420

Adjacent sequences: A056547 A056548 A056549 * A056551 A056552 A056553

Keyword

nonn,more

Author

Asher Auel, Jun 06 2000

Extensions

More terms from Jud McCranie, Jul 04 2000

a(19)-a(24) from Donovan Johnson, Dec 29 2008

a(25) from Donovan Johnson, Jun 16 2011

Status

approved