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A059404
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Numbers with different exponents in their prime factorizations.
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27
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Donald Alan Morrison, Table of n, a(n) for n = 1..10000
Donald Alan Morrison, Sage program
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FORMULA
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A062760(a(n)) > 1, i.e., a(n)/(A007947(a(n))^A051904(a(n)) = a(n)/A062759(n) > 1.
A071625(a(n)) > 1. - Michael S. Branicky, Sep 01 2022
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EXAMPLE
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440 is in the sequence because 440 = 2^3*5*11 and it has two distinct exponents, 3 and 1.
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PROG
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(PARI) is(n)=#Set(factor(n)[, 2])>1 \\ Charles R Greathouse IV, Sep 18 2015
(Python)
from sympy import factorint
def ok(n): return len(set(factorint(n).values())) > 1
print([k for k in range(190) if ok(k)]) # Michael S. Branicky, Sep 01 2022
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CROSSREFS
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Cf. A003557, A007947, A051904, A062759, A062760, A071625.
Sequence in context: A317711 A359890 A323055 * A303946 A360246 A242416
Adjacent sequences: A059401 A059402 A059403 * A059405 A059406 A059407
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KEYWORD
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nonn,easy
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AUTHOR
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Labos Elemer, Jul 18 2001
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STATUS
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approved
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