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A317394 Positive integers that have exactly four representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317394 #4 Jul 27 2018 10:41:28
%S A317394 211,261,421,426,441,484,535,540,591,621,634,667,683,691,715,726,732,
%T A317394 761,771,776,778,794,818,853,862,871,925,970,979,987,989,1011,1021,
%U A317394 1023,1038,1074,1086,1105,1114,1141,1171,1176,1184,1190,1197,1222,1261,1266
%N A317394 Positive integers that have exactly four representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317394 Alois P. Heinz, <a href="/A317394/b317394.txt">Table of n, a(n) for n = 1..20000</a>
%F A317394 A317241(a(n)) = 4.
%p A317394 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317394       for p in numtheory[factorset](n-1) minus s while r<5
%p A317394         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<5, r, 5)
%p A317394       fi
%p A317394     end:
%p A317394 a:= proc(n) option remember; local k; for k from
%p A317394      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>4 do od; k
%p A317394     end:
%p A317394 seq(a(n), n=1..100);
%Y A317394 Column k=4 of A317390.
%Y A317394 Cf. A317241.
%K A317394 nonn
%O A317394 1,1
%A A317394 _Alois P. Heinz_, Jul 27 2018