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A309783
Numbers that are sums of one or more consecutive positive triangular numbers in more than one way.
3
10, 36, 55, 64, 100, 120, 136, 164, 210, 276, 361, 435, 460, 514, 560, 596, 676, 760, 1176, 1225, 1320, 1326, 1460, 1484, 1485, 1505, 1540, 1684, 1736, 1770, 1891, 1936, 2014, 2080, 2145, 2180, 2314, 2485, 2596, 2890, 3156, 3244, 3275, 3364, 3486, 3570, 3710, 3916
OFFSET
1,1
COMMENTS
The first number that is the sum in three ways is 2180. The first that is the sum in four ways is 10053736. - Robert Israel, Aug 20 2019
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000 (first 2759 terms from Robert Israel)
FORMULA
A307666(a(n)) > 1.
MAPLE
N:= 10000: # for terms <= N
V:= Vector(N):
for i from 1 while i*(i+1)/2 <= N do
s:= i*(i+1)*(i+2)/6;
for j from i-1 to 0 by -1 do
t:= j*(j+1)*(j+2)/6;
if s-t > N then break fi;
V[s-t]:= V[s-t]+1
od;
od:
select(t -> V[t]>1, [$1..N]); # Robert Israel, Aug 20 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 17 2019
STATUS
approved