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A051760
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Numbers that are simultaneously a sum of distinct factorials and of the form a^b with b >= 3.
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4
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Paul.Jobling(AT)WhiteCross.com, Aug 10 2000
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STATUS
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approved
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