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%I #11 Sep 06 2018 19:27:33
%S 1,3,5,7,11,13,17,19,23,29,31,35,41,43,47,49,59,61,67,71,73,79,83,89,
%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271
%N Minimum Heinz number of a factorization of n into factors > 1.
%C The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%p a:= proc(n) option remember; `if`(n=1, 1, min(ithprime(n),
%p seq(ithprime(d)*a(n/d), d=numtheory[divisors](n) minus {1, n})))
%p end:
%p seq(a(n), n=1..60); # _Alois P. Heinz_, Sep 05 2018
%t facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];
%t Table[Min[Times@@Prime/@#&/@facs[n]],{n,100}]
%Y Cf. A000040, A001055, A007716, A056239, A064988, A162247, A215366, A246868.
%K nonn
%O 1,2
%A _Gus Wiseman_, Sep 05 2018
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