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A047994
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Unitary totient (or unitary phi) function uphi(n).
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31
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1, 1, 2, 3, 4, 2, 6, 7, 8, 4, 10, 6, 12, 6, 8, 15, 16, 8, 18, 12, 12, 10, 22, 14, 24, 12, 26, 18, 28, 8, 30, 31, 20, 16, 24, 24, 36, 18, 24, 28, 40, 12, 42, 30, 32, 22, 46, 30, 48, 24, 32, 36, 52, 26, 40, 42, 36, 28, 58, 24, 60, 30, 48, 63, 48, 20, 66, 48, 44, 24, 70
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Unitary convolution of A076479 and A000027. - R. J. Mathar, Apr 13 2011
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math. Zeitschr. 74 (1960) 66-80
S. R. Finch, Unitarism and infinitarism.
M. Lal, Iterates of the unitary totient function, Math. Comp., 28 (1974), 301-302.
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FORMULA
| If n = Product p_i^e_i, uphi(n) = Product (p_i^e_i - 1).
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EXAMPLE
| a(12)=a(3)a(4)=2*3=6.
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MAPLE
| A047994 := proc(n)
if n = 1 then
return 1;
end if;
a := 1 ;
for f in ifactors(n)[2] do
a := a*(op(1, f)^op(2, f)-1) ;
end do:
a ;
end proc:
seq(A047994(n), n=1..20) ; # R. J. Mathar, Dec 22 2011
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MATHEMATICA
| uphi[n_] := (Times @@ (Table[ #[[1]]^ #[[2]] - 1, {1} ] & /@ FactorInteger[n]))[[1]]; Table[ uphi[n], {n, 2, 75}] (from Robert G. Wilson v Sep 06 2004)
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PROG
| (PARI) A047994(n)=prod(i=1, #n=factor(n)~, n[1, i]^n[2, i]-1)
(Haskell)
a047994 n = f n 1 where
f 1 uph = uph
f x uph = f (x `div` sppf) (uph * (sppf - 1)) where sppf = a028233 x
-- Reinhard Zumkeller, Aug 17 2011
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CROSSREFS
| Cf. A049865, A003271, A028233.
Sequence in context: A206369 A178970 A172054 * A193024 A153038 A117009
Adjacent sequences: A047991 A047992 A047993 * A047995 A047996 A047997
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KEYWORD
| nonn,easy,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu).
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