A273058 Numbers having pairwise coprime exponents in their canonical prime factorization.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 1

Author

Giuseppe Coppoletta, May 14 2016

Keywords

• nonn

Comments

The complement of A072413.

Examples

			36 is not a term because 36 = 2^2 * 3^2 and gcd(2,2) = 2 > 1.
360 is a term because 360 = 2^3 * 3^2 * 5 and gcd(3,2) = gcd(2,1) = 1.
10800 is not a term because 10800 = 2^4 * 3^3 * 5^2 and gcd(4,2) > 1
		

Links

• Giuseppe Coppoletta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005361, A072411, A130091, A072413.

Programs

Mathematica

Select[Range@ 120, LCM @@ # == Times @@ # &@ Map[Last, FactorInteger@ #] &] (* Michael De Vlieger, May 15 2016 *)

PARI

is(n)=my(f=factor(n)[,2]); factorback(f)==lcm(f) \\ Charles R Greathouse IV, Jan 14 2017

Sage

def d(n):
    v=factor(n)[:]; L=len(v); diff=prod(v[j][1] for j in range(L)) - lcm([v[j][1] for j in range(L)])
    return diff
[k for k in (1..100) if d(k)==0]

Formula

A005361(a(n)) = A072411(a(n)).