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A317396 Positive integers that have exactly six representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317396 #4 Jul 27 2018 11:01:22
%S A317396 664,1956,2058,2092,2094,2283,2381,2388,2432,2466,2533,2624,2701,2775,
%T A317396 2822,2853,2976,3070,3193,3220,3316,3326,3436,3442,3461,3485,3529,
%U A317396 3568,3571,3576,3620,3746,3784,3785,3797,3826,3839,3913,4005,4026,4031,4213,4234
%N A317396 Positive integers that have exactly six representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317396 Alois P. Heinz, <a href="/A317396/b317396.txt">Table of n, a(n) for n = 1..20000</a>
%F A317396 A317241(a(n)) = 6.
%p A317396 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317396       for p in numtheory[factorset](n-1) minus s while r<7
%p A317396         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<7, r, 7)
%p A317396       fi
%p A317396     end:
%p A317396 a:= proc(n) option remember; local k; for k from
%p A317396      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>6 do od; k
%p A317396     end:
%p A317396 seq(a(n), n=1..100);
%Y A317396 Column k=6 of A317390.
%Y A317396 Cf. A317241.
%K A317396 nonn
%O A317396 1,1
%A A317396 _Alois P. Heinz_, Jul 27 2018