

A056550


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


15



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
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OFFSET

1,2


LINKS



FORMULA

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


EXAMPLE



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[n1]; 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



CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



