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A046642 Numbers n such that n and number of divisors d(n) are relatively prime. 14
1, 3, 4, 5, 7, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 100, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A009191(a(n)) = 1.

Numbers n such that tau(n)^phi(n) == 1 mod n, where tau(n) is the number of divisors of n (A000005) and phi(n) is the Euler phi function (A000010). - Michel Lagneau, Nov 20 2012

Density is at least 4/Pi^2 = 0.405... since A056911 is a subsequence, and at most 1/2 since all even numbers in this sequence are squares. The true value seems to be around 0.4504. - Charles R Greathouse IV, Mar 27 2013

They are called anti-tau numbers by Zelinsky (see link) and their density is 3/Pi^2 (theorem 57 page 15). - Michel Marcus, May 31 2015

LINKS

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

Joshua Zelinsky, Tau Numbers: A Partial Proof of a Conjecture and Other Results, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8.

MATHEMATICA

Select[ Range[200], CoprimeQ[#, DivisorSigma[0, #]] &] (* Jean-Fran├žois Alcover, Oct 20 2011 *)

PROG

(Haskell)

a046642 n = a046642_list !! (n-1)

a046642_list = map (+ 1) $ elemIndices 1 a009191_list

-- Reinhard Zumkeller, Aug 14 2011

(PARI) is(n)=gcd(numdiv(n), n)==1 \\ Charles R Greathouse IV, Mar 27 2013

CROSSREFS

Cf. A009191, A009230.

Sequence in context: A091428 A047499 A082378 * A140826 A081735 A227231

Adjacent sequences:  A046639 A046640 A046641 * A046643 A046644 A046645

KEYWORD

nonn,nice,easy

AUTHOR

Labos Elemer

STATUS

approved

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Last modified April 26 12:07 EDT 2019. Contains 322472 sequences. (Running on oeis4.)