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Maximum Heinz number of a strict factorization of n into factors > 1.
9

%I #7 Sep 07 2018 04:44:08

%S 1,3,5,7,11,15,17,21,23,33,31,39,41,51,55,57,59,69,67,87,85,93,83,111,

%T 97,123,115,129,109,165,127,159,155,177,187,195,157,201,205,231,179,

%U 255,191,237,253,249,211,285,227,319,295,303,241,345,341,357,335,327

%N Maximum Heinz number of a strict factorization of n into factors > 1.

%C The Heinz number of a factorization (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

%e The strict factorizations of 80 are (2*4*10), (2*5*8), (2*40), (4*20), (5*16), (8*10), (80), with Heinz numbers 609, 627, 519, 497, 583, 551, 409 respectively, so a(80) = 627.

%t facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];

%t Table[Max[Times@@Prime/@#&/@Select[facs[n],UnsameQ@@#&]],{n,100}]

%Y Cf. A001055, A007716, A045778, A056239, A080688, A162247, A215366, A246868, A318871, A318954.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 05 2018