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A317400 Positive integers that have exactly ten representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes. 2

%I

%S 11306,13289,13693,16402,16446,16491,16699,17031,17113,17116,17263,

%T 17576,18412,18602,19825,20023,20411,21022,21256,21676,21936,22271,

%U 22543,22716,22764,23038,23233,23332,23353,23580,23599,23886,24036,24053,24064,24531,24646

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

%H Alois P. Heinz, <a href="/A317400/b317400.txt">Table of n, a(n) for n = 1..20000</a>

%F A317241(a(n)) = 10.

%p b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;

%p for p in numtheory[factorset](n-1) minus s while r<11

%p do r:= r+b((n-1)/p, s union {p}) od; `if`(r<11, r, 11)

%p fi

%p end:

%p a:= proc(n) option remember; local k; for k from

%p `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>10 do od; k

%p end:

%p seq(a(n), n=1..100);

%Y Column k=10 of A317390.

%Y Cf. A317241.

%K nonn

%O 1,1

%A _Alois P. Heinz_, Jul 27 2018

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Last modified May 13 15:38 EDT 2021. Contains 343860 sequences. (Running on oeis4.)