A317393 Positive integers that have exactly three representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

43, 61, 91, 111, 121, 124, 171, 184, 187, 205, 221, 231, 256, 265, 267, 268, 274, 277, 281, 283, 291, 311, 323, 326, 331, 337, 371, 373, 375, 379, 386, 411, 412, 427, 428, 435, 443, 451, 456, 457, 471, 474, 475, 482, 491, 494, 505, 507, 508, 511, 519, 521, 523

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=3 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<4
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<4, r, 4)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>3 do od; k
    end:
seq(a(n), n=1..100);

Formula

A317241(a(n)) = 3.