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A097706
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Part of n composed of prime factors of form 4k+3.
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18
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1, 1, 3, 1, 1, 3, 7, 1, 9, 1, 11, 3, 1, 7, 3, 1, 1, 9, 19, 1, 21, 11, 23, 3, 1, 1, 27, 7, 1, 3, 31, 1, 33, 1, 7, 9, 1, 19, 3, 1, 1, 21, 43, 11, 9, 23, 47, 3, 49, 1, 3, 1, 1, 27, 11, 7, 57, 1, 59, 3, 1, 31, 63, 1, 1, 33, 67, 1, 69, 7, 71, 9, 1, 1, 3, 19, 77, 3, 79, 1, 81, 1, 83, 21
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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MAPLE
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a:= n-> mul(`if`(irem(i[1], 4)=3, i[1]^i[2], 1), i=ifactors(n)[2]):
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MATHEMATICA
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a[n_] := Product[{p, e} = pe; If[Mod[p, 4] == 3, p^e, 1], {pe, FactorInteger[n]}]; Array[a, 100] (* Jean-François Alcover, Jun 16 2015, updated May 29 2019 *)
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PROG
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(PARI) a(n)=local(f); f=factor(n); prod(k=1, matsize(f)[1], if(f[k, 1]%4<>3, 1, f[k, 1]^f[k, 2]))
(Python)
from sympy import factorint
from operator import mul
def a072436(n):
f=factorint(n)
return 1 if n == 1 else reduce(mul, [1 if i%4==3 else i**f[i] for i in f])
(Python)
from math import prod
from sympy import factorint
def A097706(n): return prod(p**e for p, e in factorint(n).items() if p & 3 == 3) # Chai Wah Wu, Jun 28 2022
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CROSSREFS
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Equivalent sequence for distinct prime factors: A170819.
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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