A272605 a(1) = 1, for n>=1 a(n) is the largest prime factor of A002182(n).

1, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 11, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 13, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 17, 17, 19, 19, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 23, 19, 23, 19

Offset

1,2

Comments

For n>=1, the largest prime factor of the n-th highly composite number.

Links

Joerg Arndt, Table of n, a(n) for n = 1..19999

Example

The first highly composite numbers with their prime factorizations:
n:  A002182(n) = [factorization]
1:  1  = []
2:  2   = [2]
3:  4   = [2^2]
4:  6   = [2 * 3]
5:  12   = [2^2 * 3]
6:  24   = [2^3 * 3]
7:  36   = [2^2 * 3^2]
8:  48   = [2^4 * 3]
9:  60   = [2^2 * 3 * 5]
10:  120   = [2^3 * 3 * 5]
11:  180   = [2^2 * 3^2 * 5]
12:  240   = [2^4 * 3 * 5]
13:  360   = [2^3 * 3^2 * 5]
14:  720   = [2^4 * 3^2 * 5]
15:  840   = [2^3 * 3 * 5 * 7]
16:  1260   = [2^2 * 3^2 * 5 * 7]
17:  1680   = [2^4 * 3 * 5 * 7]
18:  2520   = [2^3 * 3^2 * 5 * 7]
19:  5040   = [2^4 * 3^2 * 5 * 7]
20:  7560   = [2^3 * 3^3 * 5 * 7]
21:  10080   = [2^5 * 3^2 * 5 * 7]
22:  15120   = [2^4 * 3^3 * 5 * 7]
23:  20160   = [2^6 * 3^2 * 5 * 7]
24:  25200   = [2^4 * 3^2 * 5^2 * 7]
25:  27720   = [2^3 * 3^2 * 5 * 7 * 11]
26:  45360   = [2^4 * 3^4 * 5 * 7]
27:  50400   = [2^5 * 3^2 * 5^2 * 7]
28:  55440   = [2^4 * 3^2 * 5 * 7 * 11]
29:  83160   = [2^3 * 3^3 * 5 * 7 * 11]
30:  110880   = [2^5 * 3^2 * 5 * 7 * 11]

Crossrefs

Sequence in context: A343118 A087182 A035453 * A235703 A366664 A097747

Adjacent sequences: A272602 A272603 A272604 * A272606 A272607 A272608

Keyword

nonn

Author

Joerg Arndt, Nov 01 2016

Status

approved