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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.

%I A317398 #4 Jul 27 2018 11:21:55
%S A317398 2991,3004,3319,3554,3928,4846,5552,5886,6293,6784,7183,7286,7396,
%T A317398 7668,7741,7743,7829,7996,8095,8121,8212,8477,8586,8614,8856,8861,
%U A317398 9096,9307,9374,9591,9626,9636,9637,9721,9738,9845,9891,9912,9934,10011,10024,10048,10251
%N 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.
%H A317398 Alois P. Heinz, <a href="/A317398/b317398.txt">Table of n, a(n) for n = 1..20000</a>
%F A317398 A317241(a(n)) = 8.
%p A317398 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317398       for p in numtheory[factorset](n-1) minus s while r<9
%p A317398         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<9, r, 9)
%p A317398       fi
%p A317398     end:
%p A317398 a:= proc(n) option remember; local k; for k from
%p A317398      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>8 do od; k
%p A317398     end:
%p A317398 seq(a(n), n=1..100);
%Y A317398 Column k=8 of A317390.
%Y A317398 Cf. A317241.
%K A317398 nonn
%O A317398 1,1
%A A317398 _Alois P. Heinz_, Jul 27 2018