A317385 Smallest positive integer that has exactly n representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

2, 1, 25, 43, 211, 638, 664, 1613, 2991, 7021, 11306, 9439, 17361, 23230, 40886, 38341, 49063, 36583, 99111, 111229, 110631, 171718, 233451, 255531, 309141, 327643, 369519, 521266, 489406, 738544, 682690, 812826, 1048594, 1015096, 2003002, 2118439, 1602360, 2204907, 2850772, 2702743, 2794198

Offset

0,1

Links

Table of n, a(n) for n=0..40.

Formula

a(n) = min { j > 0 : A317241(j) = n }.

Example

a(1) = 1: 1.
a(2) = 25: 1 + 2 * (1 + 11) = 1 + 3 * (1 + 7) = 25.
a(3) = 43: 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:= proc(n) option remember; local k;
      for k while n<>b(k, {}) do od; k
    end:
seq(a(n), n=0..15);

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_, k_] := Module[{h, p, q = 0}, p[_] = {}; While[Length[p[k]] < n, q++; h = b[q, {}]; p[h] = Append[p[h], q]]; p[k][[n]]];
a[k_] := If[k == 0, 2, A[1, k]];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jul 14 2021, after Alois P. Heinz in A317390 *)

Crossrefs

Row n=1 of A317390.

Cf. A317241, A317384.

Sequence in context: A013317 A010256 A087452 * A366048 A098878 A235031

Adjacent sequences: A317382 A317383 A317384 * A317386 A317387 A317388

Keyword

nonn

Author

Alois P. Heinz, Jul 26 2018

Status

approved