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A059404 Numbers with different exponents in their prime factorizations. 28
12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Former name: Numbers k such that k/(largest power of squarefree kernel of k) is larger than 1.

Complement of A072774 (powers of squarefree numbers).

Also numbers k = p(1)^alpha(1)* ... * p(r)^alpha(r) such that RootMeanSquare(alpha(1), ..., alpha(r)) is not an integer. - Ctibor O. Zizka, Sep 19 2008

LINKS

Donald Alan Morrison, Table of n, a(n) for n = 1..10000

Donald Alan Morrison, Sage program

FORMULA

A062760(a(n)) > 1, i.e., a(n)/(A007947(a(n))^A051904(a(n)) = a(n)/A062759(n) > 1.

EXAMPLE

440 is in the sequence because 440 = 2^3*5*11 and it has two distinct exponents, 3 and 1.

PROG

(PARI) is(n)=#Set(factor(n)[, 2])>1 \\ Charles R Greathouse IV, Sep 18 2015

CROSSREFS

Cf. A003557, A007947, A051904, A062759, A062760.

Sequence in context: A200511 A317711 A323055 * A303946 A242416 A317616

Adjacent sequences:  A059401 A059402 A059403 * A059405 A059406 A059407

KEYWORD

nonn,easy

AUTHOR

Labos Elemer, Jul 18 2001

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)