A064615 Numbers of the form m * 6^k for k >= 0 and m > 0 with gcd(m, 6) = 1.

1, 5, 6, 7, 11, 13, 17, 19, 23, 25, 29, 30, 31, 35, 36, 37, 41, 42, 43, 47, 49, 53, 55, 59, 61, 65, 66, 67, 71, 73, 77, 78, 79, 83, 85, 89, 91, 95, 97, 101, 102, 103, 107, 109, 113, 114, 115, 119, 121, 125, 127, 131, 133, 137, 138, 139, 143, 145, 149, 150, 151, 155

Offset: 1

Author

Reinhard Zumkeller, Sep 25 2001

Keywords

• nonn

Comments

These are the fixed points of A064614, a permutation of natural numbers: A064614(a(n)) = a(n), for all n.

Numbers n such that exponent of highest power of 2 dividing n is equal to exponent of highest power of 3 dividing n. - Juri-Stepan Gerasimov, Sep 01 2016

All primes >3 are terms. - Zak Seidov, Sep 02 2016

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A064614.

Programs

Magma

[n: n in [1..200] |Valuation(n, 2) eq Valuation(n, 3)]; // Vincenzo Librandi, Sep 02 2016

Maple

q:= n-> is(padic[ordp](n, 2)=padic[ordp](n, 3)):
select(q,[$1..200])[];  # Alois P. Heinz, Oct 28 2021

Mathematica

okQ[n_] := IntegerExponent[n, 2] == IntegerExponent[n, 3];
Select[Range[200], okQ] (* Jean-François Alcover, Oct 28 2021 *)

PARI

is(n)=valuation(n,2)==valuation(n,3) \\ Charles R Greathouse IV, Sep 02 2016

Formula

a(n) = 5n/2 + O(log n). - Charles R Greathouse IV, Sep 02 2016