A100394 a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).

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, 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, 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

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

Maple

f:= n -> numtheory:-pi(max(numtheory:-factorset(2*ithprime(n)+1))):
map(f, [$1..100]); # Robert Israel, Jul 08 2018

Prog

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

Crossrefs

Cf. A006530, A023590.

Sequence in context: A094758 A283971 A348173 * A178783 A156671 A072006

Adjacent sequences: A100391 A100392 A100393 * A100395 A100396 A100397

Keyword

nonn

Author

Labos Elemer, Dec 16 2004

Status

approved