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

Author

Joerg Arndt, Nov 01 2016

Keywords

• nonn

Comments

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

Examples

			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]
		

Links

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