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A084127 Prime factor >= other prime factor of n-th semiprime. 43

%I #31 Aug 05 2022 20:03:05

%S 2,3,3,5,7,5,7,11,5,13,11,17,7,19,13,23,7,17,11,19,29,31,13,23,37,11,

%T 41,17,43,29,13,31,47,19,53,37,23,59,17,11,61,41,43,19,67,47,71,13,29,

%U 73,31,79,53,23,83,13,59,89,61,37,17,97,67,101,29,41,103,19,71,107,43,31

%N Prime factor >= other prime factor of n-th semiprime.

%C Largest nontrivial divisor of n-th semiprime. [_Juri-Stepan Gerasimov_, Apr 18 2010]

%C Greater of the prime factors of A001358(n). - _Jianing Song_, Aug 05 2022

%H Zak Seidov, <a href="/A084127/b084127.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>

%F a(n) = A006530(A001358(n)).

%F a(n) = A001358(n)/A020639(A001358(n)). [corrected by _Michel Marcus_, Jul 18 2020]

%F a(n) = A001358(n)/A084126(n).

%t FactorInteger[#][[-1, 1]]& /@ Select[Range[1000], PrimeOmega[#] == 2&] (* _Jean-François Alcover_, Nov 17 2021 *)

%o (Haskell)

%o a084127 = a006530 . a001358 -- _Reinhard Zumkeller_, Nov 25 2012

%o (PARI) lista(nn) = {for (n=2, nn, if (bigomega(n)==2, f = factor(n); print1(f[length(f~),1], ", ")););} \\ _Michel Marcus_, Jun 05 2013

%Y Cf. A001358 (the semiprimes), A084126 (lesser of the prime factors of the semiprimes).

%Y Cf. A014673, A061299, A068318, A087718, A087794, A089994, A089995, A096932, A106550, A106554, A108542, A126663, A131284, A138510, A138511.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 15 2003

%E Corrected by _T. D. Noe_, Nov 15 2006

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