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

Author

Mohammad K. Azarian

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000010, A048855, A113638.

Programs

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

Mathematica

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

Python

from sympy import isprime
def A014684(n): return n-int(isprime(n)) # Chai Wah Wu, Oct 14 2023

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

Extensions

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