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Numbers having more than one representation as a sum of the minimal number of triangular numbers, A000217.
3

%I #10 Jun 16 2015 14:06:32

%S 16,17,19,23,26,31,32,33,35,40,41,42,44,46,47,51,52,54,56,59,62,63,68,

%T 71,72,74,75,76,77,80,81,82,85,86,89,94,95,96,98,103,104,106,107,109,

%U 111,113,116,117,118,121,122,123,124,125,126,128,129,131,133,134

%N Numbers having more than one representation as a sum of the minimal number of triangular numbers, A000217.

%C A258257(a(n)) > 1.

%C Complement of A258264.

%H Giovanni Resta, <a href="/A258265/b258265.txt">Table of n, a(n) for n = 1..10000</a>

%t t[n_] := n*(n + 1)/2; ok[n_] := Block[{k = 1, t, tt = t /@ Range[Sqrt[2*n]]}, While[{} == (r = IntegerPartitions[n, {k}, tt]), k++]; 1 < Length@r]; Select[ Range@ 1000, ok] (* _Giovanni Resta_, Jun 09 2015 *)

%Y Cf. A258257, A258264.

%K nonn

%O 1,1

%A _Martin Renner_, May 25 2015