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

1,2

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

Table of n, a(n) for n=1..58.

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)

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

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 *)

Prog

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

Crossrefs

Cf. A000040, A008578, A065091, A002322.

Sequence in context: A074918 A175524 A073579 * A065091 A160656 A176997

Adjacent sequences: A006002 A006003 A006004 * A006006 A006007 A006008

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved