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A215405 Largest prime factor of the n-th n-almost prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 15 11:44 EDT 2021. Contains 345048 sequences. (Running on oeis4.)