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

1,1

Links

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

Formula

A317241(a(n)) = 8.

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);

Crossrefs

Column k=8 of A317390.

Cf. A317241.

Sequence in context: A159731 A221725 A205241 * A346221 A253962 A253955

Adjacent sequences: A317395 A317396 A317397 * A317399 A317400 A317401

Keyword

nonn

Author

Alois P. Heinz, Jul 27 2018

Status

approved