A319316 -id:A319316 - cp's OEIS frontend

8, 16, 17, 20, 24, 25, 26, 32, 34, 35, 40, 41, 44, 48, 49, 50, 52, 53, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 96, 97, 98, 104, 106, 107, 116, 128, 129, 130, 131, 132, 133, 134, 136, 137, 140, 142, 143, 144, 145, 146, 148, 149, 150, 151

Offset: 1

Jianing Song, Sep 17 2018

nonn

Numbers k such that the highest power of 12 dividing n! is determined by the highest power of 3 dividing n!.
Note that A054861 and A090616 are both asymptotic to a(n) = n/2 + O(log(n)), nevertheless, it seems that the number of k such that A090616(k) is bigger predominates. Conjecture: the ratio of k <= N such that A090616(k) >A054861(k) tends to 1 as N tends to infinity, while the ratio of k <= N such thatA090616(k) < A054861(k) and A090616(k) = A054861(k) both tend to 0.
Number of k in range [0, N] such that A090616(k) =, < or > A054861(k):
  N    A090616(k) = A054861(k)   A090616(k) < A054861(k)   A090616(k) > A054861(k)
10^2               38                        26                        37
10^3              344                       228                       429
10^4             2703                      2227                      5071
10^5            23003                     19892                     57106
10^6           203478                    185152                    611371
10^7          1762288                   1726062                   6511651

			The highest power of 3 dividing 8! is 3^2, while the highest power of 4 dividing 8! is 4^3, so 8 is a term, and the highest power of 12 dividing 8! is 12^2.
The highest power of 3 dividing 16! is 3^6, while the highest power of 4 dividing 16! is 4^7, so 16 is a term, and the highest power of 12 dividing 16! is 12^6.

Jianing Song, Table of n, a(n) for n = 1..5071 (all terms <= 10000)

Cf. A217445 (k such that A090616(k) = A054861(k)), A319316 (k such that A090616(k) < A054861(k)).

isA319317(n)=(n-vecsum(digits(n, 2)))\2>(n-vecsum(digits(n, 3)))\2

cp's OEIS Frontend

A319317 Numbers k such that A090616(k) > A054861(k).

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