cp's OEIS Frontend

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

%I A056550 #56 May 04 2025 18:20:37
%S A056550 1,2,8,11,17,63,180,259,818,2161,4441,8305,11998,694218,3447076,
%T A056550 4393603,57402883,73459800,121475393,2068420025,5577330586,
%U A056550 13320495021,35297649260,138630178659,988671518737,1424539472772,3028785109162,13702718147734,21320824383487
%N A056550 Numbers k such that Sum_{j=1..k} sigma(j) is divisible by k, where sigma(j) = sum of divisors of j (A000203).
%F A056550 Values of k for which A024916(k)/k is an integer.
%e A056550 a(3) = 8 is in the sequence because A024916(8) / 8 = 56 / 8 = 7 is an integer. [_Jaroslav Krizek_, Dec 07 2009]
%p A056550 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;
%t A056550 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 *)
%t A056550 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 *)
%o A056550 (PARI) is(n)=sum(k=1,n,n\k*k)%n==0 \\ _Charles R Greathouse IV_, Feb 14 2013
%Y A056550 Cf. A000203, A024916, A168133, A168132.
%K A056550 nonn,more,hard
%O A056550 1,2
%A A056550 _Asher Auel_, Jun 06 2000
%E A056550 More terms from _Jud McCranie_, Jul 04 2000
%E A056550 a(19)-a(24) from _Donovan Johnson_, Dec 29 2008
%E A056550 a(25) from _Donovan Johnson_, Jun 16 2011
%E A056550 a(26) from _Jud McCranie_, Dec 17 2024
%E A056550 a(27) from _Jud McCranie_, Dec 22 2024
%E A056550 a(28) from _Jud McCranie_, Apr 03 2025
%E A056550 a(29) from _Jud McCranie_, May 04 2025