A317241 -id:A317241 - cp's OEIS frontend

A317397 Positive integers that have exactly seven representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

1613, 3321, 3336, 3368, 3741, 3914, 3979, 4082, 4126, 4219, 4561, 4777, 4798, 4824, 4929, 4936, 4948, 5083, 5314, 5371, 5559, 5656, 5825, 5877, 5946, 5986, 6096, 6109, 6111, 6291, 6303, 6376, 6644, 6651, 6673, 6700, 6711, 6786, 6883, 6886, 6917, 6920, 7036

Offset: 1

Alois P. Heinz, Jul 27 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Column k=7 of A317390.

Cf. A317241.

b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
      for p in numtheory[factorset](n-1) minus s while r<8
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<8, r, 8)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>7 do od; k
    end:
seq(a(n), n=1..100);

A317241(a(n)) = 7.

A317398 Positive integers that have exactly eight representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

Original entry on oeis.org

2991, 3004, 3319, 3554, 3928, 4846, 5552, 5886, 6293, 6784, 7183, 7286, 7396, 7668, 7741, 7743, 7829, 7996, 8095, 8121, 8212, 8477, 8586, 8614, 8856, 8861, 9096, 9307, 9374, 9591, 9626, 9636, 9637, 9721, 9738, 9845, 9891, 9912, 9934, 10011, 10024, 10048, 10251

Offset: 1

Alois P. Heinz, Jul 27 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Column k=8 of A317390.

Cf. A317241.

b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
      for p in numtheory[factorset](n-1) minus s while r<9
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<9, r, 9)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>8 do od; k
    end:
seq(a(n), n=1..100);

A317241(a(n)) = 8.

A317399 Positive integers that have exactly nine representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

Original entry on oeis.org

7021, 7162, 8053, 8737, 9178, 9556, 10126, 10858, 10861, 10866, 11113, 11133, 11363, 11740, 12076, 12111, 12666, 13168, 13210, 13339, 13573, 13729, 14037, 14366, 14411, 14691, 15250, 15478, 15569, 15653, 15726, 15922, 16066, 16113, 16116, 16386, 16459, 16644

Offset: 1

Alois P. Heinz, Jul 27 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Column k=9 of A317390.

Cf. A317241.

b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
      for p in numtheory[factorset](n-1) minus s while r<10
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<10, r, 10)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>9 do od; k
    end:
seq(a(n), n=1..100);

A317241(a(n)) = 9.

A317400 Positive integers that have exactly ten representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

Original entry on oeis.org

11306, 13289, 13693, 16402, 16446, 16491, 16699, 17031, 17113, 17116, 17263, 17576, 18412, 18602, 19825, 20023, 20411, 21022, 21256, 21676, 21936, 22271, 22543, 22716, 22764, 23038, 23233, 23332, 23353, 23580, 23599, 23886, 24036, 24053, 24064, 24531, 24646

Offset: 1

Alois P. Heinz, Jul 27 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Column k=10 of A317390.

Cf. A317241.

b:= proc(n, s) option remember; local p, r; if n=1 then 1 else r:=0;
      for p in numtheory[factorset](n-1) minus s while r<11
        do r:= r+b((n-1)/p, s union {p}) od; `if`(r<11, r, 11)
      fi
    end:
a:= proc(n) option remember; local k; for k from
     `if`(n=1, 1, 1+a(n-1)) while b(k, {})<>10 do od; k
    end:
seq(a(n), n=1..100);

A317241(a(n)) = 10.

cp's OEIS Frontend

A317397 Positive integers that have exactly seven representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

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A317398 Positive integers that have exactly eight representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

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A317399 Positive integers that have exactly nine representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

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Maple

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A317400 Positive integers that have exactly ten representations of the form 1 + p1 * (1 + p2* ... * (1 + p_j)...), where [p1, ..., p_j] is a (possibly empty) list of distinct primes.

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Author

Keywords

Links

Crossrefs

Programs

Maple

Formula