A141115 -id:A141115 - cp's OEIS frontend

A141113 Positive integers k such that d(d(k)) divides k, where d(k) is the number of divisors of k.

1, 2, 4, 6, 12, 15, 16, 20, 21, 24, 27, 28, 32, 33, 36, 39, 40, 44, 48, 51, 52, 56, 57, 60, 64, 68, 69, 72, 76, 80, 84, 87, 88, 90, 92, 93, 96, 104, 108, 111, 112, 116, 120, 123, 124, 126, 128, 129, 132, 136, 141, 144, 148, 150, 152, 156, 159, 164, 172, 176, 177, 180

Offset: 1

Leroy Quet, Jun 04 2008

nonn

			28 has 6 divisors and 6 has 4 divisors. 4 divides 28, so 28 is in the sequence.

Jinyuan Wang, Table of n, a(n) for n = 1..10000

Cf. A000005 (tau), A010553, A141114, A141115.

with(numtheory): a:=proc(n) if `mod`(n, tau(tau(n))) = 0 then n else end if end proc: seq(a(n),n=1..200); # Emeric Deutsch, Jun 05 2008

Select[Range[200],Divisible[#,DivisorSigma[0,DivisorSigma[0,#]]]&] (* Harvey P. Dale, Feb 05 2012 *)

is(k) = k%numdiv(numdiv(k)) == 0; \\ Jinyuan Wang, Feb 19 2019

More terms from Emeric Deutsch, Jun 05 2008

A141114 Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.

Original entry on oeis.org

1, 3, 5, 7, 8, 9, 10, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 45, 46, 47, 49, 53, 55, 58, 59, 61, 62, 63, 65, 67, 71, 73, 74, 75, 77, 79, 81, 82, 83, 85, 86, 89, 91, 94, 95, 97, 99, 100, 101, 103, 105, 106, 107, 109, 113, 115, 117, 118, 119, 121

Offset: 1

Leroy Quet, Jun 04 2008

nonn

Includes all primes, squares of odd primes, and squarefree semiprimes coprime to 3. - Robert Israel, Dec 16 2019

			26 has 4 divisors and 4 has 3 divisors. 3 is coprime to 26, so 26 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A010553, A141113, A141115.

[k:k in [1..130]|Gcd(k,#Divisors(#Divisors(k))) eq 1]; // Marius A. Burtea, Dec 16 2019

filter:= proc(n) uses numtheory;
  igcd(tau(tau(n)), n) = 1
end proc:
select(filter, [$1..200]); # Robert Israel, Dec 16 2019

Select[Range[200], GCD[DivisorSigma[0, DivisorSigma[0, # ]], # ] == 1 &] (* Stefan Steinerberger, Jun 05 2008 *)

is(n) = gcd(numdiv(numdiv(n)), n)==1 \\ Felix Fröhlich, Dec 16 2019

More terms from Stefan Steinerberger, Jun 05 2008

cp's OEIS Frontend

A141113 Positive integers k such that d(d(k)) divides k, where d(k) is the number of divisors of k.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions