This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115647 #16 Mar 19 2025 10:23:02
%S A115647 1,3,6,120,153,5886,40470,41041,40279800
%N A115647 Triangular numbers that are sums of distinct factorials.
%C A115647 Factorials 0! and 1! are not considered distinct.
%C A115647 A115944(a(n)) > 0; subsequence of A059590. - _Reinhard Zumkeller_, Feb 02 2006
%C A115647 If there are any terms beyond 40279800 they must be larger than 48!. - _Jon E. Schoenfield_, Aug 04 2006
%H A115647 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_3">Triangular Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 83-125. See also <a href="https://doi.org/10.1007/978-981-97-2465-9_16">Fascinating Factorials</a>, Ch. 16, 411-442.
%e A115647 1 = T(1) = 1!.
%e A115647 3 = T(2) = 2!+1!.
%e A115647 6 = T(3) = 3!.
%e A115647 120 = T(15) = 5!.
%e A115647 153 = T(17) = 5!+4!+3!+2!+1!.
%e A115647 5886 = T(108) = 7!+6!+5!+3!.
%e A115647 40470 = T(284) = 8!+5!+4!+3!.
%e A115647 41041 = T(286) = 8!+6!+1!.
%e A115647 40279800 = T(8975) = 11!+9!+5!.
%t A115647 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
%Y A115647 Cf. A025494.
%K A115647 nonn
%O A115647 1,2
%A A115647 _Giovanni Resta_, Jan 27 2006