A215776 Second-largest prime factor of the n-th number that is a product of exactly n primes.

1, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 5, 2, 3, 3, 3, 3, 2, 5, 5, 2, 3, 3, 2, 3, 7, 3, 3, 3, 5, 5, 5, 3, 2, 3, 2, 5, 5, 3, 3, 3, 7, 2, 3, 3, 3, 7, 5, 2, 5, 5, 5, 3, 2, 3, 5, 3, 7, 3, 5, 2, 5, 5, 3, 3, 2, 3, 7, 3, 3, 3, 3, 5, 7, 2, 5, 7, 11, 2, 7, 3, 5, 5, 5, 3, 3, 3

Offset

1,2

Comments

This is to A215405 as 2nd largest prime factor is to largest (greatest) prime factor. Technically, the prime numbers are "1-almost prime."

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A087039(A101695(n)).

Example

a(2) = 2 because the 2nd number that is a product of exactly 2 primes
(semiprime) is 6 = 2*3, so 2 is the 2nd largest of those two prime factors.
a(4) = 2 because the 4th number that is a product of exactly 4 primes is 40 = 2*2*2*5, so 2 is the 2nd largest of those two distinct prime factors {2,5}. This requires clarity in "distinct prime factors" versus merely "prime factors."
a(87) = 3 because the 87th number that is a product of 87 primes is 5048474222710691433572990976 = 2^84 3^2 29, and 3 is the 2nd largest prime factor.

Maple

A215776 := proc(n)
    A087039(A101695(n)) ;
end proc: # R. J. Mathar, Sep 14 2012

Crossrefs

Cf. A087039, A101695, A215405.

Sequence in context: A086411 A105528 A076225 * A339085 A140887 A132423

Adjacent sequences: A215773 A215774 A215775 * A215777 A215778 A215779

Keyword

nonn

Author

Jonathan Vos Post, Aug 23 2012

Extensions

Corrected by R. J. Mathar, Sep 14 2012

More terms from Lars Blomberg, Mar 02 2016

Status

approved