A367004 -id:A367004 - cp's OEIS frontend

A367003 a(n) is the largest prime factor of n*2^n-1.

1, 7, 23, 7, 53, 383, 179, 89, 271, 3413, 2503, 2137, 59, 367, 1433, 41, 15803, 59729, 26423, 11161, 1559, 12611, 9187523, 127867, 119837257, 11527, 2360833, 43969, 2339, 32212254719, 257503, 616318177, 260587, 127873, 682902239, 44939, 69660839431, 1185617

Offset: 1

Sean A. Irvine, Oct 31 2023

nonn

Amiram Eldar, Table of n, a(n) for n = 1..865

Cf. A003261, A006530, A005420, A367002, A367004, A366899.

a[n_] := FactorInteger[n*2^n - 1][[-1, 1]]; Array[a, 40] (* Amiram Eldar, Oct 29 2024 *)

a(n) = A006530(A003261(n)).

A367007 Number of distinct prime factors of n*2^n + 1.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 3, 3, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 4, 4, 3, 2, 4, 4, 4, 4, 4, 4, 2, 3, 5, 5, 3, 2, 5, 2, 3, 3, 3, 3, 3, 4, 4, 5, 4, 4, 5, 5, 4, 2, 6, 3, 6, 3, 5, 4, 3, 5, 5, 4, 4, 7, 3, 3, 6, 5, 7, 4, 4, 5, 5, 5, 5, 5, 3, 5, 4, 4, 4, 6, 4, 4, 4, 5, 4, 6, 6

Offset: 0

Sean A. Irvine, Oct 31 2023

nonn

The numbers n*2^n+1 are called Cullen numbers.

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

Cf. A002064, A001221, A367004, A367005, A367006.

Table[PrimeNu[n*2^n + 1], {n, 0, 100}] (* Amiram Eldar, Jan 06 2024 *)

a(n) = omega(n*2^n + 1); \\ Amiram Eldar, Jan 06 2024

a(n) = omega(n*2^n + 1) = A001221(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

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A367003 a(n) is the largest prime factor of n*2^n-1.

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A367007 Number of distinct prime factors 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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A367005 a(n) is the largest prime factor of n*2^n+1 for n>0, and a(0)=1.

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