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a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).
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%I #19 Jun 14 2022 06:59:32

%S 3,4,5,3,9,2,4,6,15,17,4,3,23,10,8,28,7,13,3,6,4,16,39,41,6,10,9,14,

%T 21,49,7,56,5,11,9,26,4,29,19,69,72,5,76,14,22,8,15,35,6,7,91,92,9,96,

%U 27,11,5,42,12,103,4,107,13,24,8,31,7,3,34,51,26,128,4,23,9,17,13,16,21,6

%N a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).

%H Robert Israel, <a href="/A100394/b100394.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000720(A006530(2*A000040(n) + 1)) = A000720(A023590(n)).

%e n=25: q = prime(25) = 97; 2*q + 1 = 195 = 3*5*13, whose greatest prime factor is 13, of which the subscript = pi(13) = 6 = a(25);

%e n=1: q = prime(1) = 2; 2*q + 1 = 5; A006530(5)=5, pi(5) = 3 = a(1).

%p f:= n -> numtheory:-pi(max(numtheory:-factorset(2*ithprime(n)+1))):

%p map(f, [$1..100]); # _Robert Israel_, Jul 08 2018

%o (PARI) a(n) = primepi(vecmax(factor(2*prime(n) + 1)[,1])); \\ _Michel Marcus_, Jul 09 2018; corrected Jun 14 2022

%Y Cf. A006530, A023590.

%K nonn

%O 1,1

%A _Labos Elemer_, Dec 16 2004