|
%I #14 Jan 31 2019 19:59:26
%S 1,8,27,32,128,729
%N Numbers that are simultaneously a sum of distinct factorials and of the form a^b with b >= 3.
%C No further terms up to 10^18. - _Robert Israel_, Jan 30 2019
%e 2! + 3! = 2^3;
%e 1! + 2! + 4! = 3^3;
%e 2! + 3! + 4! = 2^5;
%e 2! + 3! + 5! = 2^7;
%e 1! + 2! + 3! + 6! = 3^6 = 9^3.
%p N:= 10^5; # to get all terms <= N
%p S:= {1}:
%p for n from 2 do
%p v:= n!;
%p if v > N then break fi;
%p S:= S union {v} union map(`+`,S,v)
%p od:
%p filter:= proc(n) local F;
%p F:= ifactors(n)[2];
%p igcd(op(map(t ->t[2],F))) >= 3
%p end proc:
%p filter(1):= true:
%p select(filter, S); # _Robert Israel_, Jan 30 2019
%Y Cf. A025494, A051761.
%K nonn,more
%O 1,2
%A Paul.Jobling(AT)WhiteCross.com, Aug 10 2000
|
