A367003 -id:A367003 - cp's OEIS frontend

A367004 a(n) is the smallest prime factor of n*2^n+1.

3, 3, 5, 5, 7, 5, 3, 3, 11, 7, 13, 13, 3, 3, 17, 17, 5, 11, 3, 3, 23, 13, 5, 5, 3, 3, 7, 29, 31, 17, 3, 3, 47, 19, 37, 37, 3, 3, 41, 41, 13, 23, 3, 3, 11, 5, 7, 7, 3, 3, 53, 7, 5591, 29, 3, 3, 5, 31, 37, 61, 3, 3, 5, 5, 67, 5, 3, 3, 7, 37, 11, 41, 3, 3, 149

Offset: 1

Sean A. Irvine, Oct 31 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..914 (terms 1..350 from Robert Israel)

Cf. A002064, A005849, A020639, A049479, A367002, A367003, A367005.

seq(min(numtheory:-factorset(n*2^n+1)), n=1..100); # Robert Israel, Nov 09 2023

Table[FactorInteger[n 2^n+1][[1,1]],{n,80}] (* Harvey P. Dale, Aug 14 2024 *)

a(n) = A020639(A002064(n)).

A367002 a(n) is the smallest prime factor of n*2^n-1.

Original entry on oeis.org

7, 23, 3, 3, 383, 5, 23, 17, 3, 3, 23, 5, 5, 7, 3, 3, 79, 13, 1879, 13, 3, 3, 47, 7, 229, 5, 3, 3, 32212254719, 263, 223, 5, 3, 3, 5, 73, 17, 1217, 3, 3, 6709, 29, 7, 71, 3, 3, 11, 97, 47, 228713, 3, 3, 5, 37, 5, 7, 3, 3, 9377, 11, 13, 479, 3, 3, 41, 5, 13, 137

Offset: 2

Sean A. Irvine, Oct 31 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 2..884 (terms 2..325 from Robert Israel)

Cf. A003261, A020639, A049479, A367003, A367004, A366899.

f:= n -> min(numtheory:-factorset(n*2^n-1)):
map(f, [$2..100]); # Robert Israel, Nov 08 2023

Table[FactorInteger[n*2^n-1][[1,1]], {n,2,69}] (* Paul F. Marrero Romero, Dec 17 2023 *)

a(n) = A020639(A003261(n)).

a(n) = 3 iff n == 4 or 5 (mod 6). - Robert Israel, Nov 08 2023

A367005 a(n) is the largest prime factor of n*2^n+1 for n>0, and a(0)=1.

Original entry on oeis.org

1, 3, 3, 5, 13, 23, 11, 23, 683, 419, 19, 1733, 199, 11833, 487, 997, 61681, 4691, 211, 5279, 7541, 1914791, 7177, 607, 5233, 6689, 2373919, 336823, 8937209, 6051013, 409, 11681, 25781083, 6031230671, 18803, 32502455213, 934861, 339016085231, 55586743

Offset: 0

Sean A. Irvine, Oct 31 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 0..865

Cf. A002064, A006530, A005420, A367003, A367004.

A367005[n_]:=FactorInteger[n*2^n+1][[-1,1]];Array[A367005,50,0] (* Paolo Xausa, Nov 09 2023 *)

a(n) = A006530(A002064(n)).

Name edited by Michel Marcus, Nov 10 2023

cp's OEIS Frontend

A367004 a(n) is the smallest prime factor of n*2^n+1.

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A367002 a(n) is the smallest prime factor of n*2^n-1.

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Maple

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A367005 a(n) is the largest prime factor of n*2^n+1 for n>0, and a(0)=1.

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Author

Keywords

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Crossrefs

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Mathematica

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