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A033913
Numbers k such that s(k) + s(k+1) + ... + s(k+6) = t(k) + t(k+1) + ... + t(k+6).
2
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
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
KEYWORD
nonn,more
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