login
A318871
Minimum Heinz number of a factorization of n into factors > 1.
18
1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 41, 43, 47, 49, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271
OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
MAPLE
a:= proc(n) option remember; `if`(n=1, 1, min(ithprime(n),
seq(ithprime(d)*a(n/d), d=numtheory[divisors](n) minus {1, n})))
end:
seq(a(n), n=1..60); # Alois P. Heinz, Sep 05 2018
MATHEMATICA
facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]];
Table[Min[Times@@Prime/@#&/@facs[n]], {n, 100}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 05 2018
STATUS
approved