A014684 In the sequence of positive integers subtract 1 from each prime number.

1, 1, 2, 4, 4, 6, 6, 8, 9, 10, 10, 12, 12, 14, 15, 16, 16, 18, 18, 20, 21, 22, 22, 24, 25, 26, 27, 28, 28, 30, 30, 32, 33, 34, 35, 36, 36, 38, 39, 40, 40, 42, 42, 44, 45, 46, 46, 48, 49, 50, 51, 52, 52, 54, 55, 56, 57, 58, 58, 60, 60, 62, 63, 64, 65, 66, 66, 68, 69, 70, 70, 72

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A005171(n) + n - 1.

a(n) = phi(n!)/phi((n-1)!). - Vladeta Jovovic, Nov 30 2002

For n > 3: a(n) = A113523(n) = A179278(n). - Reinhard Zumkeller, Jul 08 2010

a(n) = n - A010051(n). - Reinhard Zumkeller, Sep 10 2013

Mathematica

Table[If[PrimeQ[n], n-1, n], {n, 100}] (* Harvey P. Dale, Aug 27 2015 *)

Prog

(Haskell)
a014684 n = n - fromIntegral (a010051 n)
-- Reinhard Zumkeller, Sep 10 2013
(Magma) [n - (IsPrime(n) select 1 else 0): n in [1..80]]; // Bruno Berselli, Jul 18 2016
(Python)
from sympy import isprime
def A014684(n): return n-int(isprime(n)) # Chai Wah Wu, Oct 14 2023

Crossrefs

Cf. A000010, A048855, A113638.

Sequence in context: A085914 A211390 A363030 * A113638 A187323 A262504

Adjacent sequences: A014681 A014682 A014683 * A014685 A014686 A014687

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

More terms from Andrew J. Gacek (andrew(AT)dgi.net)

Status

approved