A215405 -id:A215405 - cp's OEIS frontend

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

Jonathan Vos Post, Aug 23 2012

nonn

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

			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.

Cf. A087039, A101695, A215405.

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

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

Corrected by R. J. Mathar, Sep 14 2012

More terms from Lars Blomberg, Mar 02 2016

A215567 Numbers k with the property that k and the k-th number which is a product of k primes have the largest prime divisor and with the same multiplicity.

Original entry on oeis.org

3, 13, 20, 42, 44, 45, 56, 60, 86, 87, 112, 119, 121

Offset: 1

Juri-Stepan Gerasimov, Aug 16 2012

			13 and the 13th 13-almost prime = 13*2^12 = 53248 have same largest prime factor = 13, with the same multiplicity, so 13 is a term.

Cf. A001222, A101695, A215405.

AlmostPrimePi[k_Integer,n_]:=...;AlmostPrime[k_,n_]:=...;
fQ[n_]:=FactorInteger[n][[-1,1]]==FactorInteger[AlmostPrime[n,n]][[-1,1]];k=1;lst={};
While[k<150,If[fQ@k,AppendTo[lst,k];Print@k];k++];lst  (* Robert G. Wilson v, Aug 27 2012 *)

a(9)-a(13) from Robert G. Wilson v, Aug 27 2012

Definition clarified by N. J. A. Sloane, Sep 04 2012

cp's OEIS Frontend

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

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