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, 1424539472772, 3028785109162, 13702718147734, 21320824383487
Offset: 1
Examples
a(3) = 8 is in the sequence because A024916(8) / 8 = 56 / 8 = 7 is an integer. [_Jaroslav Krizek_, Dec 07 2009]
Programs
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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;
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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 *)
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PARI
is(n)=sum(k=1,n,n\k*k)%n==0 \\ Charles R Greathouse IV, Feb 14 2013
Formula
Values of k for which A024916(k)/k is an integer.
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
a(26) from Jud McCranie, Dec 17 2024
a(27) from Jud McCranie, Dec 22 2024
a(28) from Jud McCranie, Apr 03 2025
a(29) from Jud McCranie, May 04 2025
Comments