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A317397 Positive integers that have exactly seven representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317397 #4 Jul 27 2018 11:09:45
%S A317397 1613,3321,3336,3368,3741,3914,3979,4082,4126,4219,4561,4777,4798,
%T A317397 4824,4929,4936,4948,5083,5314,5371,5559,5656,5825,5877,5946,5986,
%U A317397 6096,6109,6111,6291,6303,6376,6644,6651,6673,6700,6711,6786,6883,6886,6917,6920,7036
%N A317397 Positive integers that have exactly seven representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317397 Alois P. Heinz, <a href="/A317397/b317397.txt">Table of n, a(n) for n = 1..20000</a>
%F A317397 A317241(a(n)) = 7.
%p A317397 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317397       for p in numtheory[factorset](n-1) minus s while r<8
%p A317397         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<8, r, 8)
%p A317397       fi
%p A317397     end:
%p A317397 a:= proc(n) option remember; local k; for k from
%p A317397      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>7 do od; k
%p A317397     end:
%p A317397 seq(a(n), n=1..100);
%Y A317397 Column k=7 of A317390.
%Y A317397 Cf. A317241.
%K A317397 nonn
%O A317397 1,1
%A A317397 _Alois P. Heinz_, Jul 27 2018