A317390 -id:A317390 - cp's OEIS frontend

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.

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.

A317537 The n-th 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.

Original entry on oeis.org

1, 29, 91, 426, 1002, 2283, 3979, 5886, 10861, 17116, 20749, 35106, 44031, 60919, 67453, 108655, 142429, 197107, 232625, 303317, 352093, 432517, 542935, 642520, 839938, 988791, 1050505, 1208559, 1612876, 1753324, 2129203, 2391496, 2735890, 3141916, 3593278

Offset: 1

Alois P. Heinz, Jul 30 2018

nonn

			a(1) = 1: 1.
a(2) = 29: 1 + 2 * (1 + 13) = 1 + 7 * (1 + 3) = 29.
a(3) = 91: 1 + 2 * (1 + 11 * (1 + 3)) = 1 + 3 * (1 + 29) = 1 + 5 * (1 + 17) = 91.

A diagonal of A317390.

Cf. A317385.

a(n) = A317390(n,n).

cp's OEIS Frontend

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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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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A317537 The n-th 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.

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