A115645 Powerful(1) numbers (A001694) that are sums of distinct factorials.

1, 8, 9, 25, 27, 32, 121, 128, 144, 729, 841, 864, 5041, 5184, 40328, 41067, 45369, 45387, 46208, 46225, 363609, 403225, 3674889, 43954688, 6230694987, 1401602635449

Offset

1,2

Comments

Factorials 0! and 1! are not considered distinct.

a(27) > 10^18, if it exists. - Amiram Eldar, Feb 24 2024

Links

Table of n, a(n) for n=1..26.

Index entries for sequences related to powerful numbers.

Example

6230694987 = 13!+10!+8!+7!+4!+2!+1! = 3^3*11^2*1381^2.

Mathematica

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
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 *)

Crossrefs

Intersection of A001694 and A059590.

Cf. A025494, A115644, A115646, A089359.

Sequence in context: A077599 A109097 A335770 * A068435 A302554 A124438

Adjacent sequences: A115642 A115643 A115644 * A115646 A115647 A115648

Keyword

nonn,more

Author

Giovanni Resta, Jan 27 2006

Status

approved