A062325 Numbers k for which phi(prime(k)) is a square.

1, 3, 7, 12, 26, 45, 55, 79, 106, 123, 211, 252, 422, 446, 595, 723, 907, 1019, 1101, 1448, 1595, 1687, 1797, 1849, 1949, 2058, 2393, 2516, 2703, 2819, 3146, 3339, 3477, 3626, 4353, 4437, 4590, 5153, 5398, 5653, 5836, 6276, 6543, 6736, 6911, 7207, 7695

Offset: 1

Author

Jason Earls, Jul 05 2001

Keywords

• easy
• nonn

Comments

Also A002496 indexed by A000040.

Examples

			79 is in the sequence because the 79th prime is 401 and phi(401) is 400 = 20^2.
595 is in the sequence because the 595th prime is 4357 and phi(4357) is 4356 = 66^2.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000720, A001912, A002496, A005574, A062325, A090693.

Programs

Mathematica

Flatten[Position[Table[IntegerQ[Sqrt[Prime[w]-1]], {w, 1, 25000}], True]]
Flatten[Position[EulerPhi[Prime[Range[8000]]],?(IntegerQ[Sqrt[#]]&)]] (* _Harvey P. Dale, Apr 23 2014 *)

PARI

for(n=1,1600, if(issquare(eulerphi(prime(n))),print(n)))

PARI

{ default(primelimit, 2*10^8); n=m=0; forprime (p=2, 2*10^8, m++; if (issquare(eulerphi(p)), write("b062325.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Formula

a(n) = A000720(A002496(n)).

A000040(a(n)) = A002496(n).

Extensions

More terms from Labos Elemer, Jul 09 2001