A317241 - OEIS

%I #18 May 26 2019 16:15:19

%S 1,0,1,1,0,1,0,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,2,0,0,0,2,1,0,1,0,1,

%T 0,0,2,1,1,2,2,1,3,1,1,1,0,1,2,0,2,2,1,1,1,0,0,1,1,1,3,1,0,1,1,0,2,1,

%U 1,1,2,1,1,1,1,1,2,0,1,1,0,0,1,1,2,1,2,2,2,1,3,1,1,1,0,0,2,1,1,1,1,1,2,1,1

%N Number of representations of n 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="/A317241/b317241.txt">Table of n, a(n) for n = 1..65536</a>

%F a(n) = 0 <=> n in { A317242 }.

%F a(n) <= A317240(n).

%e a(25) = 2: 1 + 2 * (1 + 11) = 1 + 3 * (1 + 7) = 25.

%e a(43) = 3: 1 + 2 * (1 + 5 * (1 + 3)) = 1 + 3 * (1 + 13) = 1 + 7 * (1 + 5) = 43.

%p b:= proc(n, s) option remember; `if`(n=1, 1,

%p       add(b((n-1)/p, s union {p}), p=numtheory[factorset](n-1) minus s))

%p     end:

%p a:= n-> b(n, {}):

%p seq(a(n), n=1..200);

%t b[n_, s_] := b[n, s] = If[n == 1, 1, Sum[If[p == 1, 0, b[(n - 1)/p, s ~Union~ {p}]], {p, FactorInteger[n - 1][[All, 1]] ~Complement~ s}]];

%t a[n_] := b[n, {}];

%t Array[a, 200] (* _Jean-François Alcover_, May 26 2019, after _Alois P. Heinz_ *)

%Y Cf. A317240, A317242, A317385.

%K nonn

%O 1,25

%A _Alois P. Heinz_, Jul 24 2018