A033913 Numbers k such that s(k) + s(k+1) + ... + s(k+6) = t(k) + t(k+1) + ... + t(k+6).

5, 11, 19, 133, 465, 1361, 1693, 205021, 317293, 2757669, 3104613, 12369341, 33468065, 187542277, 535082701, 821575373, 1310332017, 1454159241, 26789967589, 45217224437

Offset

1,1

Comments

a(21) > 10^11. - Donovan Johnson, Aug 15 2011

Links

Table of n, a(n) for n=1..20.

Formula

Here s(k) = sigma(k) - k, t(k) = |s(k) - k|.

Mathematica

Select[Range[500000], Total[DivisorSigma[1, Range[#, #+6]]-Range[#, #+6]] == Total[ Abs[ DivisorSigma[ 1, Range[#, #+6]]-2Range[#, #+6]]]&]  (* Harvey P. Dale, Aug 14 2011 *)

Prog

(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

Crossrefs

Cf. A001065, A033880, A033910, A033911, A033912.

Sequence in context: A297365 A128927 A145934 * A088124 A344549 A345353

Adjacent sequences: A033910 A033911 A033912 * A033914 A033915 A033916

Keyword

nonn,more

Author

Naohiro Nomoto

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005

a(10)-a(20) from Donovan Johnson, Aug 15 2011

Status

approved