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 A115645 #10 Feb 24 2024 11:04:40
%S A115645 1,8,9,25,27,32,121,128,144,729,841,864,5041,5184,40328,41067,45369,
%T A115645 45387,46208,46225,363609,403225,3674889,43954688,6230694987,
%U A115645 1401602635449
%N A115645 Powerful(1) numbers (A001694) that are sums of distinct factorials.
%C A115645 Factorials 0! and 1! are not considered distinct.
%C A115645 a(27) > 10^18, if it exists. - _Amiram Eldar_, Feb 24 2024
%H A115645 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e A115645 6230694987 = 13!+10!+8!+7!+4!+2!+1! = 3^3*11^2*1381^2.
%t A115645 pwfQ[n_] := n==1 || Min[Last /@ FactorInteger@n] > 1; fac=Range[20]!;lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 20]); If[pwfQ[n], AppendTo[lst, n]], {k, 2^20-1}]; lst
%t A115645 q[n_] := Module[{k = n, m = 2, r, ans = True}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r > 1, ans = False; Break[]]; m++]; ans]; With[{max = 2^20-1}, Select[Union[Flatten[Table[i^2*j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}]]], q]] (* _Amiram Eldar_, Feb 24 2024 *)
%Y A115645 Intersection of A001694 and A059590.
%Y A115645 Cf. A025494, A115644, A115646, A089359.
%K A115645 nonn,more
%O A115645 1,2
%A A115645 _Giovanni Resta_, Jan 27 2006