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A317399 Positive integers that have exactly nine representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317399 #4 Jul 27 2018 11:31:15
%S A317399 7021,7162,8053,8737,9178,9556,10126,10858,10861,10866,11113,11133,
%T A317399 11363,11740,12076,12111,12666,13168,13210,13339,13573,13729,14037,
%U A317399 14366,14411,14691,15250,15478,15569,15653,15726,15922,16066,16113,16116,16386,16459,16644
%N A317399 Positive integers that have exactly nine representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317399 Alois P. Heinz, <a href="/A317399/b317399.txt">Table of n, a(n) for n = 1..20000</a>
%F A317399 A317241(a(n)) = 9.
%p A317399 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317399       for p in numtheory[factorset](n-1) minus s while r<10
%p A317399         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<10, r, 10)
%p A317399       fi
%p A317399     end:
%p A317399 a:= proc(n) option remember; local k; for k from
%p A317399      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>9 do od; k
%p A317399     end:
%p A317399 seq(a(n), n=1..100);
%Y A317399 Column k=9 of A317390.
%Y A317399 Cf. A317241.
%K A317399 nonn
%O A317399 1,1
%A A317399 _Alois P. Heinz_, Jul 27 2018