A055742 Numbers k such that k and EulerPhi(k) have same number of prime factors, counted without multiplicity.

1, 3, 4, 5, 8, 14, 16, 17, 18, 21, 22, 26, 28, 32, 33, 35, 36, 38, 39, 44, 45, 46, 50, 52, 54, 55, 56, 57, 58, 63, 64, 65, 69, 72, 74, 75, 76, 82, 87, 88, 91, 92, 94, 95, 100, 104, 106, 108, 111, 112, 115, 116, 117, 118, 119, 123, 128, 133, 135, 141, 144, 145, 146, 148

Offset: 1

Author

Labos Elemer, Jul 11 2000

Keywords

• nonn

Examples

			Known Fermat primes 3 and 5 are terms because their phi value is divisible only by 2. Several composites are also here, such as {50, 999, 1000} with prime factors (2,5), (3,37) and (2,5); their phi values, {20, 648, 400}, also have 2 prime factors: (2,5), (2,3), (2,5).
		

Links

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

Crossrefs

Cf. A001221, A000010, A055744, A070418.

Programs

Haskell

a055742 n = a055742_list !! (n-1)
a055742_list = [x | x <- [1..], a001221 x == a001221 (a000010 x)]
-- Reinhard Zumkeller, Apr 14 2015

Mathematica

Select[Range[200],PrimeNu[#]==PrimeNu[EulerPhi[#]]&] (* Harvey P. Dale, Sep 12 2014 *)

PARI

is(n)=my(f=factor(n)); #f~ == omega(eulerphi(f)) \\ Charles R Greathouse IV, Mar 01 2017

Formula

A001221(A000010(n)) = A001221(n).

Extensions

Definition clarified by Harvey P. Dale, Sep 12 2014