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

1,2

Comments

The complement of A072413.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A005361, A072411, A130091, A072413.

Sequence in context: A269393 A269394 A273884 * A044922 A346447 A273883

Adjacent sequences: A273055 A273056 A273057 * A273059 A273060 A273061

Keyword

nonn

Author

Giuseppe Coppoletta, May 14 2016

Status

approved