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A273058 Numbers having pairwise coprime exponents in their canonical prime factorization. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A273883 A132145

Adjacent sequences:  A273055 A273056 A273057 * A273059 A273060 A273061

KEYWORD

nonn

AUTHOR

Giuseppe Coppoletta, May 14 2016

STATUS

approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)