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

1,2

Links

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

Formula

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

Example

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).

Mathematica

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

Prog

(Haskell)
a055742 n = a055742_list !! (n-1)
a055742_list = [x | x <- [1..], a001221 x == a001221 (a000010 x)]
-- Reinhard Zumkeller, Apr 14 2015
(PARI) is(n)=my(f=factor(n)); #f~ == omega(eulerphi(f)) \\ Charles R Greathouse IV, Mar 01 2017

Crossrefs

Cf. A001221, A000010, A055744, A070418.

Sequence in context: A358356 A368800 A039020 * A263041 A216888 A362218

Adjacent sequences: A055739 A055740 A055741 * A055743 A055744 A055745

Keyword

nonn

Author

Labos Elemer, Jul 11 2000

Extensions

Definition clarified by Harvey P. Dale, Sep 12 2014

Status

approved