A317241 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.

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, 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, 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

Offset

1,25

Links

Alois P. Heinz, Table of n, a(n) for n = 1..65536

Formula

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

a(n) <= A317240(n).

Example

a(25) = 2: 1 + 2 * (1 + 11) = 1 + 3 * (1 + 7) = 25.
a(43) = 3: 1 + 2 * (1 + 5 * (1 + 3)) = 1 + 3 * (1 + 13) = 1 + 7 * (1 + 5) = 43.

Maple

b:= proc(n, s) option remember; `if`(n=1, 1,
      add(b((n-1)/p, s union {p}), p=numtheory[factorset](n-1) minus s))
    end:
a:= n-> b(n, {}):
seq(a(n), n=1..200);

Mathematica

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}]];
a[n_] := b[n, {}];
Array[a, 200] (* Jean-François Alcover, May 26 2019, after Alois P. Heinz *)

Crossrefs

Cf. A317240, A317242, A317385.

Sequence in context: A024941 A219492 A285796 * A361499 A287299 A374207

Adjacent sequences: A317238 A317239 A317240 * A317242 A317243 A317244

Keyword

nonn

Author

Alois P. Heinz, Jul 24 2018

Status

approved