A317395 - OEIS

%I #4 Jul 27 2018 10:47:46

%S 638,848,921,969,1002,1026,1106,1156,1191,1248,1276,1310,1326,1341,

%T 1431,1444,1480,1499,1548,1592,1641,1730,1764,1772,1786,1856,1888,

%U 1911,1996,2005,2025,2038,2050,2053,2061,2121,2129,2131,2133,2146,2171,2224,2256,2258

%N Positive integers that have exactly five 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="/A317395/b317395.txt">Table of n, a(n) for n = 1..20000</a>

%F A317241(a(n)) = 5.

%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<6

%p         do r:= r+b((n-1)/p, s union {p}) od; `if`(r<6, r, 6)

%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, {})<>5 do od; k

%p     end:

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

%Y Column k=5 of A317390.

%Y Cf. A317241.

%K nonn

%O 1,1

%A _Alois P. Heinz_, Jul 27 2018