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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS No further terms up to 10^18. - Robert Israel, Jan 30 2019 LINKS 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 Cf. A025494, A051761. Sequence in context: A304291 A056824 A297868 * A213519 A066215 A086213 Adjacent sequences:  A051757 A051758 A051759 * A051761 A051762 A051763 KEYWORD nonn,more AUTHOR Paul.Jobling(AT)WhiteCross.com, Aug 10 2000 STATUS approved

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Last modified August 4 02:19 EDT 2021. Contains 346441 sequences. (Running on oeis4.)