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A170818
a(n) is the product of primes (with multiplicity) of form 4*k+1 that divide n.
10
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
OFFSET
1,5
COMMENTS
Completely multiplicative with a(p) = p if p = 4k+1 and a(p) = 1 otherwise. - Tom Edgar, Mar 05 2015
LINKS
FORMULA
a(n) = n/A072438(n). - Michel Marcus, Mar 05 2015
MAPLE
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
MATHEMATICA
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 *)
PROG
(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, prod
def a072438(n):
f = factorint(n)
return 1 if n == 1 else prod(i**f[i] for i in f if i % 4 != 1)
def a(n): return n//a072438(n) # Indranil Ghosh, May 08 2017
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Dec 22 2009
STATUS
approved