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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.
15
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 24 2018
STATUS
approved