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Largest prime factor of sequence of numbers of the form p*q (p, q distinct primes).
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%I #23 Oct 28 2024 09:36:02

%S 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,

%T 29,13,31,47,19,53,37,23,59,17,61,41,43,19,67,47,71,13,29,73,31,79,53,

%U 23,83,59,89,61,37,17,97,67,101,29,41,103,19,71,107,43,31,109,73,17

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

%H Reinhard Zumkeller, <a href="/A070647/b070647.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = A006881(n)/A096916(n). - _Amiram Eldar_, Oct 28 2024

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

%t 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 *)

%o (Haskell)

%o a070647 = a006530 . a006881 -- _Reinhard Zumkeller_, Sep 23 2011

%o (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

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

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, May 13 2002