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%I #21 Jul 29 2021 09:29:14
%S 5,11,19,133,465,1361,1693,205021,317293,2757669,3104613,12369341,
%T 33468065,187542277,535082701,821575373,1310332017,1454159241,
%U 26789967589,45217224437
%N Numbers k such that s(k) + s(k+1) + ... + s(k+6) = t(k) + t(k+1) + ... + t(k+6).
%C a(21) > 10^11. - _Donovan Johnson_, Aug 15 2011
%F Here s(k) = sigma(k) - k, t(k) = |s(k) - k|.
%t Select[Range[500000],Total[DivisorSigma[1,Range[#,#+6]]-Range[#,#+6]] == Total[ Abs[ DivisorSigma[ 1,Range[#,#+6]]-2Range[#,#+6]]]&] (* _Harvey P. Dale_, Aug 14 2011 *)
%o (PARI) l=vector(7,n,abs(sigma(n)-2*n)-sigma(n)+n);l[7]=0;sc=sum(n=1,7,l[n]);for(n=7,1000000,m=sigma(n)-2*n;d=abs(m)-m-n;i=(n-1)%7+1;sc=sc-l[i]+d;l[i]=d;if(sc==0,print1(n-6,","))) \\ C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005
%Y Cf. A001065, A033880, A033910, A033911, A033912.
%K nonn,more
%O 1,1
%A _Naohiro Nomoto_
%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005
%E a(10)-a(20) from _Donovan Johnson_, Aug 15 2011
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