A210719 Numbers n for which phi(n) is different from phi(m) for all m < n.

1, 3, 5, 7, 11, 13, 15, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 69, 71, 73, 79, 81, 83, 85, 87, 89, 97, 101, 103, 107, 109, 113, 121, 123, 127, 129, 131, 137, 139, 141, 143, 149, 151, 157, 159, 161, 163, 167, 173, 177, 179, 181, 185

Offset: 1

Author

Antti Karttunen, Dec 16 2012

Keywords

• nonn

Comments

In the definition, phi(n) is Euler's totient function (A000010).

Also, the positions where phi(n) attains a new value.

All terms are odd.

The sequence of odd primes (A065091) is a subsequence.

Examples

			7 is in the sequence because phi(7) = 6, and 7 is the smallest n such that phi(n) = 6 (the sequence A000010 starts 1, 1, 2, 2, 4, 2, 6, ...).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A090127.

Programs

Haskell

a210719 n = a210719_list !! (n-1)
a210719_list = f (zip [1..] a000010_list) [] where
   f ((i,x):ixs) phis | x `elem` phis = f ixs phis
                      | otherwise     = i : f ixs (x : phis)
-- Reinhard Zumkeller, Dec 18 2012

Mathematica

nn = 185; s = EulerPhi[Range[nn]]; Select[Range[nn], ! MemberQ[Take[s, # - 1], s[[#]]] &] (* T. D. Noe, Dec 17 2012 *)

PARI

is_a210719(n) = {local(i,r,p);r=1;p=eulerphi(n);for(i=1,n-1,if(eulerphi(i)==p,r=0));r} \\ Michael B. Porter, Dec 16 2012

Formula

A090127(n) = A000010(a(n)).