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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. 14
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 26 2019, after Alois P. Heinz *)

CROSSREFS

Cf. A317240, A317242, A317385.

Sequence in context: A024941 A219492 A285796 * A287299 A100699 A108921

Adjacent sequences:  A317238 A317239 A317240 * A317242 A317243 A317244

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 24 2018

STATUS

approved

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Last modified May 9 15:21 EDT 2021. Contains 343742 sequences. (Running on oeis4.)