A070647 Largest prime factor of sequence of numbers of the form p*q (p, q distinct primes).

3, 5, 7, 5, 7, 11, 13, 11, 17, 7, 19, 13, 23, 17, 11, 19, 29, 31, 13, 23, 37, 11, 41, 17, 43, 29, 13, 31, 47, 19, 53, 37, 23, 59, 17, 61, 41, 43, 19, 67, 47, 71, 13, 29, 73, 31, 79, 53, 23, 83, 59, 89, 61, 37, 17, 97, 67, 101, 29, 41, 103, 19, 71, 107, 43, 31, 109, 73, 17

Offset: 1

Author

Benoit Cloitre, May 13 2002

Keywords

• easy
• nonn

Examples

			6 = 2*3 is the first number of the form p*q (p, q distinct primes) hence a(1) = 3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A006881, A084127, A096916, A195758.

Programs

Haskell

a070647 = a006530 . a006881 -- Reinhard Zumkeller, Sep 23 2011

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1};f1[n_]:=Min[First/@FactorInteger[n]];f2[n_]:=Max[First/@FactorInteger[n]];lst={};Do[If[f[n],AppendTo[lst,f2[n]]],{n,0,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Apr 10 2010 *)

PARI

go(x)=my(v=List()); forprime(p=2, sqrtint(x\1), forprime(q=p+1, x\p, listput(v, [p*q,q]))); apply(v->v[2], vecsort(Vec(v),1)) \\ Charles R Greathouse IV, Sep 14 2015

Formula

a(n) = P(A006881(n)) where P(x) = A006530(x) is the largest prime factor of x.

a(n) = A006881(n)/A096916(n). - Amiram Eldar, Oct 28 2024