A215405 Largest prime factor of the n-th n-almost prime.

2, 3, 3, 5, 3, 7, 5, 3, 7, 11, 5, 5, 13, 3, 7, 11, 5, 17, 7, 5, 19, 13, 3, 23, 7, 7, 11, 5, 17, 7, 11, 5, 19, 29, 13, 31, 5, 13, 3, 23, 7, 7, 37, 11, 5, 17, 11, 7, 41, 11, 5, 17, 19, 43, 29, 7, 13, 13, 31, 5, 47, 19, 13, 3, 23, 53, 7, 7, 37

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 09 2012

Keywords

• nonn

Comments

Technically, the prime numbers are "1-almost prime."

Prime(m) (m>=1) occurs first at index n = 1, 2, 4, 6, 10, 13, 18, 21, 24, 34, 36, 43, 49, 54, 61, 66, 75, 79, 91, 97, 101, 107, 113, 124, 138, 144, 148, 157, 162, 167, 187, 194, 202, 207, 224, 229,... in the sequence. - R. J. Mathar, Aug 09 2012

n <= a(n) at 1, 2, 3, 4, 6, 10, 13,...

n < 2*a(n) at n = 1, 2, 3, 4, 6, 7, 9, 10, 13, 16, 18, 21, 22, 24, 29, 33, 34, 36, 40, 43, 49, 54, 55, 59, 61, 66, 69,...

Also largest prime factor of A122943(n) for n>1. - Eric Desbiaux, Mar 20 2016

Examples

			a(2) = 3 because the 2nd 2-almost prime (semiprime, A001358) is 6 = 2 * 3, the largest prime factor there being 3.
a(3) = 3 because the 3rd 3-almost prime (A014612) is 18 = 2 * 3^2, the largest prime factor there being 3.
a(4) = 5 because the 4th 4-almost prime (A014613) is 40 = 2^3 * 5, the largest prime factor there being 5.
		

Crossrefs

Cf. A078841, A101695.

Programs

Maple

A215405 := proc(n)
        A006530(A101695(n)) ;
end proc: # R. J. Mathar, Aug 09 2012

Extensions

Corrected by R. J. Mathar, Aug 09 2012