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

1,1

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

Links

Table of n, a(n) for n=1..69.

Example

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.

Maple

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

Crossrefs

Cf. A078841, A101695.

Sequence in context: A152864 A152984 A177980 * A064921 A064917 A154727

Adjacent sequences: A215402 A215403 A215404 * A215406 A215407 A215408

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 09 2012

Extensions

Corrected by R. J. Mathar, Aug 09 2012

Status

approved