cp's OEIS Frontend

A317391 Positive integers that have a unique representation of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

%I A317391 #9 Jul 14 2021 09:14:54
%S A317391 1,3,4,6,8,9,10,12,13,14,16,17,18,19,20,21,22,24,30,32,34,38,39,42,44,
%T A317391 45,46,48,53,54,55,58,59,60,62,64,65,68,69,70,72,73,74,75,76,79,80,83,
%U A317391 84,86,90,92,93,94,98,99,100,101,102,104,105,107,108,109
%N A317391 Positive integers that have a unique representation of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.
%H A317391 Alois P. Heinz, <a href="/A317391/b317391.txt">Table of n, a(n) for n = 1..20000</a>
%F A317391 A317241(a(n)) = 1.
%p A317391 b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
%p A317391       for p in numtheory[factorset](n-1) minus s while r<2
%p A317391         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<2, r, 2)
%p A317391       fi
%p A317391     end:
%p A317391 a:= proc(n) option remember; local k; for k from
%p A317391      `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>1 do od; k
%p A317391     end:
%p A317391 seq(a(n), n=1..100);
%Y A317391 Column k=1 of A317390.
%Y A317391 Cf. A317241.
%K A317391 nonn
%O A317391 1,2
%A A317391 _Alois P. Heinz_, Jul 27 2018