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A115647
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Triangular numbers that are sums of distinct factorials.
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2
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OFFSET
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1,2
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COMMENTS
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Factorials 0! and 1! are not considered distinct.
If there are any terms beyond 40279800 they must be larger than 48!. - Jon E. Schoenfield, Aug 04 2006
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LINKS
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EXAMPLE
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1 = T(1) = 1!.
3 = T(2) = 2!+1!.
6 = T(3) = 3!.
120 = T(15) = 5!.
153 = T(17) = 5!+4!+3!+2!+1!.
5886 = T(108) = 7!+6!+5!+3!.
40470 = T(284) = 8!+5!+4!+3!.
41041 = T(286) = 8!+6!+1!.
40279800 = T(8975) = 11!+9!+5!.
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MATHEMATICA
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triQ[n_] := IntegerQ@Sqrt[8n+1]; fac=Reverse@Range[21]!; lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 21]); If[triQ[n], AppendTo[lst, n]; Print[{n, k}]], {k, 2^21-1}]; Union@lst
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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