A215405 - OEIS

%I #34 Apr 06 2016 01:52:07

%S 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,

%T 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,

%U 13,13,31,5,47,19,13,3,23,53,7,7,37

%N Largest prime factor of the n-th n-almost prime.

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

%C 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

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

%C 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,...

%C Also largest prime factor of A122943(n) for n>1. - _Eric Desbiaux_, Mar 20 2016

%e a(2) = 3 because the 2nd 2-almost prime (semiprime, A001358) is 6 = 2 * 3, the largest prime factor there being 3.

%e a(3) = 3 because the 3rd 3-almost prime (A014612) is 18 = 2 * 3^2, the largest prime factor there being 3.

%e a(4) = 5 because the 4th 4-almost prime (A014613) is 40 = 2^3 * 5, the largest prime factor there being 5.

%p A215405 := proc(n)

%p         A006530(A101695(n)) ;

%p end proc: # _R. J. Mathar_, Aug 09 2012

%Y Cf. A078841, A101695.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Aug 09 2012

%E Corrected by _R. J. Mathar_, Aug 09 2012