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A053165
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4th-power-free part of n.
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12
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 2, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 3, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69, 70, 71, 72, 73
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OFFSET
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1,2
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LINKS
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FORMULA
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Dirichlet g.f.: zeta(4s)*zeta(s-1)/zeta(4s-4). The Dirichlet convolution of this sequence with A008835 is A000203. - R. J. Mathar, Apr 05 2011
(End)
Multiplicative with a(p^e) = p^(e mod 4). - Amiram Eldar, Sep 07 2020
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MATHEMATICA
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f[p_, e_] := p^Mod[e, 4]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *)
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PROG
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(Python)
from operator import mul
from functools import reduce
from sympy import factorint
return 1 if n <=1 else reduce(mul, [p**(e % 4) for p, e in factorint(n).items()])
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CROSSREFS
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A003961, A059897 are used to express relationship between terms of this sequence.
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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