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A033915
Numbers n such that s(n)+s(n+1)+...+s(n+10) = t(n)+t(n+1)+...+t(n+10).
0
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
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
Sequence in context: A161714 A049743 A339865 * A192358 A123848 A340669
KEYWORD
nonn,more
EXTENSIONS
2 more terms from Ryan Propper, Aug 24 2005
a(9)-a(12) from Donovan Johnson, Aug 15 2011
STATUS
approved