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A317392 Positive integers that have exactly two representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317392 #5 Jul 27 2018 10:29:28
%S A317392 25,29,37,40,41,49,51,52,67,71,77,85,87,88,89,97,103,112,115,123,125,
%T A317392 126,127,130,137,139,145,146,148,149,155,157,161,169,175,181,183,186,
%U A317392 191,199,202,209,214,217,222,223,229,232,235,238,239,241,243,248,249
%N A317392 Positive integers that have exactly two representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317392 Alois P. Heinz, <a href="/A317392/b317392.txt">Table of n, a(n) for n = 1..20000</a>
%F A317392 A317241(a(n)) = 2.
%p A317392 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317392       for p in numtheory[factorset](n-1) minus s while r<3
%p A317392         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<3, r, 3)
%p A317392       fi
%p A317392     end:
%p A317392 a:= proc(n) option remember; local k; for k from
%p A317392      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>2 do od; k
%p A317392     end:
%p A317392 seq(a(n), n=1..100);
%Y A317392 Column k=2 of A317390.
%Y A317392 Cf. A317241.
%K A317392 nonn
%O A317392 1,1
%A A317392 _Alois P. Heinz_, Jul 27 2018