A051760 Numbers that are simultaneously a sum of distinct factorials and of the form a^b with b >= 3.

1, 8, 27, 32, 128, 729

Offset: 1

Author

Paul.Jobling(AT)WhiteCross.com, Aug 10 2000

Keywords

• nonn
• more

Comments

No further terms up to 10^18. - Robert Israel, Jan 30 2019

Examples

			2! + 3! = 2^3;
1! + 2! + 4! = 3^3;
2! + 3! + 4! = 2^5;
2! + 3! + 5! = 2^7;
1! + 2! + 3! + 6! = 3^6 = 9^3.
		

Crossrefs

Cf. A025494, A051761.

Programs

Maple

N:= 10^5; # to get all terms <= N
S:= {1}:
for n from 2 do
v:= n!;
if v > N then break fi;
S:= S union {v} union map(`+`,S,v)
od:
filter:= proc(n) local F;
  F:= ifactors(n)[2];
  igcd(op(map(t ->t[2],F))) >= 3
end proc:
filter(1):= true:
select(filter, S); # Robert Israel, Jan 30 2019