OFFSET
0,3
COMMENTS
For all n, omega(a(n)) = Omega(a(n)). The prime factorization of each term gives the least part primes of all partitions of n into prime parts.
Product of all terms in row n of A333238. - Alois P. Heinz, Mar 16 2020
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..6269
EXAMPLE
a(2) = 2 because [2] is the only prime partition of 2. a(5) = 10 because the prime partitions of 5 are [2,3] and [5], so the products of all distinct least part primes is 2*5 = 10.
MAPLE
b:= proc(n, p, t) option remember; `if`(n=0, 1, `if`(p>n, 0, (q->
add(b(n-p*j, q, 1), j=1..n/p)*t^p+b(n, q, t))(nextprime(p))))
end:
a:= n-> (p-> mul(`if`(coeff(p, x, i)>0, i, 1), i=2..n))(b(n, 2, x)):
seq(a(n), n=0..55); # Alois P. Heinz, Mar 12 2020
MATHEMATICA
a[0] = 1; a[n_] := Times @@ Union[Min /@ IntegerPartitions[n, All, Prime[ Range[PrimePi[n]]]]];
a /@ Range[0, 55] (* Jean-François Alcover, Nov 01 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
David James Sycamore, Mar 08 2020
STATUS
approved