A318953 Maximum Heinz number of a strict factorization of n into factors > 1.

1, 3, 5, 7, 11, 15, 17, 21, 23, 33, 31, 39, 41, 51, 55, 57, 59, 69, 67, 87, 85, 93, 83, 111, 97, 123, 115, 129, 109, 165, 127, 159, 155, 177, 187, 195, 157, 201, 205, 231, 179, 255, 191, 237, 253, 249, 211, 285, 227, 319, 295, 303, 241, 345, 341, 357, 335, 327

Offset: 1

Author

Gus Wiseman, Sep 05 2018

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];
Table[Max[Times@@Prime/@#&/@Select[facs[n],UnsameQ@@#&]],{n,100}]