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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 (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-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

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Last modified September 9 20:10 EDT 2024. Contains 375765 sequences. (Running on oeis4.)