A287010 Triangle T(n,m): floor(log(A002110(n))/log(prime(m))).

1, 2, 1, 4, 3, 2, 7, 4, 3, 2, 11, 7, 4, 3, 3, 14, 9, 6, 5, 4, 4, 18, 11, 8, 6, 5, 5, 4, 23, 14, 9, 8, 6, 6, 5, 5, 27, 17, 11, 9, 8, 7, 6, 6, 6, 32, 20, 14, 11, 9, 8, 7, 7, 7, 6, 37, 23, 16, 13, 10, 10, 9, 8, 8, 7, 7, 42, 26, 18, 15, 12, 11, 10, 10, 9, 8, 8, 8

Offset

1,2

Comments

Row n lists the largest power e of the prime divisors p_m of primorial p_n# such that p_m^e <= p_n#.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (Rows 1 <= n <= 150).

Example

For n = 3, A002110(n) = 30 = 2 * 3 * 5; floor(log_2(30)) = 4, floor(log_3(30)) = 3, floor(log_5(30)) = 2, thus row 3 = {4, 3, 2}.
Triangle begins:
   1:   1
   2:   2   1
   3:   4   3   2
   4:   7   4   3   2
   5:  11   7   4   3   3
   6:  14   9   6   5   4   4
   7:  18  11   8   6   5   5   4
   8:  23  14   9   8   6   6   5   5
   9:  27  17  11   9   8   7   6   6   6
  10:  32  20  14  11   9   8   7   7   7   6
  11:  37  23  16  13  10  10   9   8   8   7   7
  12:  42  26  18  15  12  11  10  10   9   8   8   8
  ...

Mathematica

Table[With[{P = Product[Prime@ i, {i, n}]}, Floor@ Log[Prime@ #, P] & /@ Range@ n], {n, 20}] // Flatten

Crossrefs

Cf. A002110, A054850.

Sequence in context: A294317 A377802 A064277 * A144330 A141155 A204922

Adjacent sequences: A287007 A287008 A287009 * A287011 A287012 A287013

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, Aug 31 2017

Status

approved