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Triangle T(n,m): floor(log(A002110(n))/log(prime(m))).
1

%I #12 Sep 04 2017 00:28:51

%S 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,

%T 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,

%U 10,10,9,8,8,7,7,42,26,18,15,12,11,10,10,9,8,8,8

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

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

%H Michael De Vlieger, <a href="/A287010/b287010.txt">Table of n, a(n) for n = 1..11325</a> (Rows 1 <= n <= 150).

%e 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}.

%e Triangle begins:

%e 1: 1

%e 2: 2 1

%e 3: 4 3 2

%e 4: 7 4 3 2

%e 5: 11 7 4 3 3

%e 6: 14 9 6 5 4 4

%e 7: 18 11 8 6 5 5 4

%e 8: 23 14 9 8 6 6 5 5

%e 9: 27 17 11 9 8 7 6 6 6

%e 10: 32 20 14 11 9 8 7 7 7 6

%e 11: 37 23 16 13 10 10 9 8 8 7 7

%e 12: 42 26 18 15 12 11 10 10 9 8 8 8

%e ...

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

%Y Cf. A002110, A054850.

%K nonn,easy,tabl

%O 1,2

%A _Michael De Vlieger_, Aug 31 2017