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A170818
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a(n) = product of primes (with multiplicity) of form 4k+1 that divide n.
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7
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1, 1, 1, 1, 5, 1, 1, 1, 1, 5, 1, 1, 13, 1, 5, 1, 17, 1, 1, 5, 1, 1, 1, 1, 25, 13, 1, 1, 29, 5, 1, 1, 1, 17, 5, 1, 37, 1, 13, 5, 41, 1, 1, 1, 5, 1, 1, 1, 1, 25, 17, 13, 53, 1, 5, 1, 1, 29, 1, 5, 61, 1, 1, 1, 65, 1, 1, 17, 1, 5, 1, 1, 73, 37, 25, 1, 1, 13, 1, 5, 1, 41, 1, 1, 85, 1, 29, 1
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OFFSET
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1,5
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COMMENTS
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Completely multiplicative with a(p) = p if p = 4k+1 and a(p) = 1 otherwise. - Tom Edgar, Mar 05 2015
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
A. Tripathi, On Pythagorean triples containing a fixed integer, Fib. Q., 46/47 (2008/2009), 331-340.
Index to divisibility sequences
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FORMULA
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a(n) = n/A072438(n). - Michel Marcus, Mar 05 2015
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MAPLE
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a:= n-> mul(`if`(irem(i[1], 4)=1, i[1]^i[2], 1), i=ifactors(n)[2]):
seq(a(n), n=1..100); # Alois P. Heinz, Jun 09 2014
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MATHEMATICA
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a[n_] := Product[{p, e} = pe; If[Mod[p, 4] == 1, p^e, 1], {pe, FactorInteger[n]}];
Array[a, 100] (* Jean-François Alcover, May 29 2019 *)
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PROG
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(PARI) a(n)=my(f=factor(n)); prod(i=1, #f~, if(f[i, 1]%4>1, 1, f[i, 1])^f[i, 2]) \\ Charles R Greathouse IV, Jun 28 2015
(Python)
from sympy import factorint
from operator import mul
def a072438(n):
f = factorint(n)
return 1 if n == 1 else reduce(mul, [1 if i%4==1 else i**f[i] for i in f])
def a(n): return n/a072438(n) # Indranil Ghosh, May 08 2017
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CROSSREFS
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Cf. A170817-A170819, A097706, A083025, A072438, A286361.
Sequence in context: A060904 A135469 A170817 * A046622 A170825 A140214
Adjacent sequences: A170815 A170816 A170817 * A170819 A170820 A170821
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane, Dec 22 2009
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STATUS
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approved
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