A006005 The odd prime numbers together with 1.

1, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The odd noncomposite numbers. Also odd primes at the beginning of the 20th century. - Omar E. Pol, Mar 19 2008

Indices at which records occur in A002322. - Artur Jasinski, Apr 05 2008

Odd numbers n such that their largest divisor <= sqrt(n) equals 1. (See A161344). - Omar E. Pol, Aug 03 2009

All k for which cos((k-1)!*Pi/k) is negative. - Gerry Martens, Jun 01 2018

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 870 [alternative scanned copy].
• S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)

Crossrefs

Cf. A000040, A008578, A065091, A002322.

Programs

Mathematica

a = {}; max = 0; Do[w = CarmichaelLambda[k]; If[w > max, AppendTo[a, k]; max = k], {k, 1, 200}]; a (* Artur Jasinski, Apr 05 2008 *)
Join[{1},Prime[Range[2,60]]] (* Harvey P. Dale, Apr 15 2019 *)

PARI

prime(n)-(n==1) \\ Charles R Greathouse IV, Aug 26 2011

Formula

a(n) = A000040(n) - A000007(n) = A000040(n) - ((-1)^A000040(n)+1)/2. - Juri-Stepan Gerasimov, Oct 25 2009

a(n) = A175524(n) for n <= 30. - Reinhard Zumkeller, Jul 12 2011