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A051760
Numbers that are simultaneously a sum of distinct factorials and of the form a^b with b >= 3.
4
1, 8, 27, 32, 128, 729
OFFSET
1,2
COMMENTS
No further terms up to 10^18. - Robert Israel, Jan 30 2019
EXAMPLE
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.
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
CROSSREFS
Sequence in context: A361268 A355038 A297868 * A131548 A373144 A373373
KEYWORD
nonn,more
AUTHOR
Paul.Jobling(AT)WhiteCross.com, Aug 10 2000
STATUS
approved