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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.

%I A317393 #4 Jul 27 2018 10:36:29
%S A317393 43,61,91,111,121,124,171,184,187,205,221,231,256,265,267,268,274,277,
%T A317393 281,283,291,311,323,326,331,337,371,373,375,379,386,411,412,427,428,
%U A317393 435,443,451,456,457,471,474,475,482,491,494,505,507,508,511,519,521,523
%N 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.
%H A317393 Alois P. Heinz, <a href="/A317393/b317393.txt">Table of n, a(n) for n = 1..20000</a>
%F A317393 A317241(a(n)) = 3.
%p A317393 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317393       for p in numtheory[factorset](n-1) minus s while r<4
%p A317393         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<4, r, 4)
%p A317393       fi
%p A317393     end:
%p A317393 a:= proc(n) option remember; local k; for k from
%p A317393      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>3 do od; k
%p A317393     end:
%p A317393 seq(a(n), n=1..100);
%Y A317393 Column k=3 of A317390.
%Y A317393 Cf. A317241.
%K A317393 nonn
%O A317393 1,1
%A A317393 _Alois P. Heinz_, Jul 27 2018