A033915 Numbers n such that s(n)+s(n+1)+...+s(n+10) = t(n)+t(n+1)+...+t(n+10).

1, 29, 57, 217, 1099, 4615, 1630311, 3827247, 108899227, 305185735, 3189176095, 50514325279

Offset

1,2

Comments

a(13) > 10^11. - Donovan Johnson, Aug 15 2011

Links

Table of n, a(n) for n=1..12.

Formula

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

Mathematica

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}]

Prog

(Python)
from sympy import divisor_sigma
def s(n): return divisor_sigma(n) - n
def t(n): return abs(s(n) - n)
def ok(n): return sum(s(i) for i in range(n, n+11)) == sum(t(i) for i in range(n, n+11))
print([m for m in range(1, 10**4) if ok(m)]) # Michael S. Branicky, Jan 29 2021

Crossrefs

Cf. A000203, A001065.

Sequence in context: A161714 A049743 A339865 * A192358 A123848 A340669

Adjacent sequences: A033912 A033913 A033914 * A033916 A033917 A033918

Keyword

nonn,more

Author

Naohiro Nomoto

Extensions

2 more terms from Ryan Propper, Aug 24 2005

a(9)-a(12) from Donovan Johnson, Aug 15 2011

Status

approved