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A065338
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a(1) = 1, a(p) = p mod 4 for p prime and a(u * v) = a(u) * a(v) for u, v > 0.
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3
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1, 2, 3, 4, 1, 6, 3, 8, 9, 2, 3, 12, 1, 6, 3, 16, 1, 18, 3, 4, 9, 6, 3, 24, 1, 2, 27, 12, 1, 6, 3, 32, 9, 2, 3, 36, 1, 6, 3, 8, 1, 18, 3, 12, 9, 6, 3, 48, 9, 2, 3, 4, 1, 54, 3, 24, 9, 2, 3, 12, 1, 6, 27, 64, 1, 18, 3, 4, 9, 6, 3, 72, 1, 2, 3, 12, 9, 6, 3, 16, 81, 2, 3, 36, 1, 6, 3, 24, 1, 18, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = (2^A007814(n)) * (3^A065339(n)). a(n) <= n. a(a(n)) = a(n). a(x) = x iff x = 2^i * 3^j for i, j >= 0. a(A003586(n)) = A003586(n). a(A065331(n)) = A065331(n).
a(A004613(n)) = 1; A065333(a(n)) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 10 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = if n = 1 then 1 else (A020639(n) mod 4) * n / A020639(n).
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EXAMPLE
| a(120) = a(2*2*2*3*5) = a(2)*a(2)*a(2)*a(3)*a(5) = 2*2*2*3*1 = 24. a(150) = a(2*3*5*5) = a(2)*a(3)*a(5)*a(5) = 2*3*1*1 = 6. a(210) = a(2*3*5*7) = a(2)*a(3)*a(5)*a(7) = 2*3*1*3 = 18.
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MATHEMATICA
| a[1] = 1; a[n_] := a[n] = Mod[p = FactorInteger[n][[1, 1]], 4]*a[n/p]; Table[ a[n], {n, 1, 100} ] (* From Jean-François Alcover, Jan 20 2012 *)
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PROG
| (Haskell)
a065338 1 = 1
a065338 n = (spf `mod` 4) * a065338 (n `div` spf) where spf = a020639 n
-- Reinhard Zumkeller, Nov 18 2011
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CROSSREFS
| A039702, A000040, A003586, A007814, A065339, A065331.
Sequence in context: A082119 A129708 A071518 * A001438 A105587 A049073
Adjacent sequences: A065335 A065336 A065337 * A065339 A065340 A065341
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KEYWORD
| mult,nice,nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 29 2001
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