cp's OEIS Frontend

A318871 Minimum Heinz number of a factorization of n into factors > 1.

%I A318871 #18 Nov 18 2024 15:06:53
%S A318871 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 A318871 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,
%U A318871 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271
%N A318871 Minimum Heinz number of a factorization of n into factors > 1.
%C A318871 The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%H A318871 Alois P. Heinz, <a href="/A318871/b318871.txt">Table of n, a(n) for n = 1..10000</a>
%e A318871 a(1) = 1 = the empty product.
%e A318871 a(12) = 35 = 5 * 7 = prime(3) * prime(4).
%e A318871 a(16) = 49 = 7^2 = prime(4)^2.
%e A318871 a(23) = 83 = prime(23).
%p A318871 a:= proc(n) option remember; `if`(n=1, 1, min(seq(a(d)*
%p A318871       ithprime(n/d), d=numtheory[divisors](n) minus {n})))
%p A318871     end:
%p A318871 seq(a(n), n=1..60);  # _Alois P. Heinz_, Sep 05 2018
%t A318871 facs[n_]:=If[n<=1,{{}},Join@@Table[(Prepend[#1,d]&)/@Select[facs[n/d],Min@@#1>=d&],{d,Rest[Divisors[n]]}]];
%t A318871 Table[Min[Times@@Prime/@#&/@facs[n]],{n,100}]
%Y A318871 Cf. A000040, A001055, A007716, A056239, A064988, A162247, A215366, A246868.
%K A318871 nonn
%O A318871 1,2
%A A318871 _Gus Wiseman_, Sep 05 2018