OFFSET
1,5
COMMENTS
a(n)=1 if n is in A068194. - Robert Israel, Apr 03 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
There is a list of all triples (including those with 0 < k < n) with n <= 16 in A309507.
MAPLE
with(numtheory):
A:=[]; M:=150; ct:=Array(0..M, 0):
for n from 1 to M do
TT:=n*(n+1);
dlis:=divisors(TT);
for d in dlis do
if (d mod 2) = 1 then e := TT/d;
mi:=min(d, e); ma:=max(d, e);
k:=(ma-mi-1)/2; m:=(ma+mi-1)/2;
# skip if k<n
if k>=n then
ct[n]:=ct[n]+1;
lprint(n, k, m);
fi;
fi;
od:
od:
[seq(ct[n], n=1..M)];
# alternative:
f:= proc(n) local t, t0, r, dmax, divs;
t:= n*(n+1);
r:= padic:-ordp(t, 2);
t0:= t/2^r;
dmax:= floor((sqrt(8*t+1)-1)/2-n);
divs:= numtheory:-divisors(t0);
nops(select(`<=`, divs, dmax)) + nops(select(`<=`, divs, dmax/2^r))
end proc:
map(f, [$1..200]); # Robert Israel, Apr 03 2020
MATHEMATICA
T[n_] := n(n+1)/2;
r[n_] := Reduce[n <= k <= m && T[n] + T[k] == T[m], {k, m}, Integers];
a[n_] := Module[{rn = r[n], r0}, r0 = rn[[0]]; Which[r0 === Or, Length[rn], r0 === And, 1, rn === False, 0, True, Print["error ", n, " ", rn]]];
Array[a, 100] (* Jean-François Alcover, Jun 08 2020 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
N. J. A. Sloane, Mar 31 2020
STATUS
approved