A033915 - OEIS

%I #17 Jan 29 2021 14:26:55

%S 1,29,57,217,1099,4615,1630311,3827247,108899227,305185735,3189176095,

%T 50514325279

%N Numbers n such that s(n)+s(n+1)+...+s(n+10) = t(n)+t(n+1)+...+t(n+10).

%C a(13) > 10^11. - _Donovan Johnson_, Aug 15 2011

%F Here s(n) = sigma(n)-n, t(n) = |s(n)-n|.

%t s[n_] := DivisorSigma[1, n] - n; t[n_] := Abs[s[n]-n]; Do[If[Sum[s[k], {k, n, n + 10}] == Sum[t[k], {k, n, n + 10}], Print[n]], {n, 1, 10^7}]

%o (Python)

%o from sympy import divisor_sigma

%o def s(n): return divisor_sigma(n) - n

%o def t(n): return abs(s(n) - n)

%o def ok(n): return sum(s(i) for i in range(n, n+11)) == sum(t(i) for i in range(n, n+11))

%o print([m for m in range(1, 10**4) if ok(m)]) # _Michael S. Branicky_, Jan 29 2021

%Y Cf. A000203, A001065.

%K nonn,more

%O 1,2

%A _Naohiro Nomoto_

%E 2 more terms from _Ryan Propper_, Aug 24 2005

%E a(9)-a(12) from _Donovan Johnson_, Aug 15 2011