A317398 Positive integers that have exactly eight representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

2991, 3004, 3319, 3554, 3928, 4846, 5552, 5886, 6293, 6784, 7183, 7286, 7396, 7668, 7741, 7743, 7829, 7996, 8095, 8121, 8212, 8477, 8586, 8614, 8856, 8861, 9096, 9307, 9374, 9591, 9626, 9636, 9637, 9721, 9738, 9845, 9891, 9912, 9934, 10011, 10024, 10048, 10251

Offset: 1

Author

Alois P. Heinz, Jul 27 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Column k=8 of A317390.

Cf. A317241.

Programs

Maple

b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
      for p in numtheory[factorset](n-1) minus s while r<9
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<9, r, 9)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>8 do od; k
    end:
seq(a(n), n=1..100);

Formula

A317241(a(n)) = 8.