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A080736
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Multiplicative function defined by a(1)=1, a(2)=0, a(2^r) = phi(2^r) (r>1), a(p^r) = phi(p^r) (p odd prime, r>=1), where phi is Euler's function A000010.
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3
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1, 0, 2, 2, 4, 0, 6, 4, 6, 0, 10, 4, 12, 0, 8, 8, 16, 0, 18, 8, 12, 0, 22, 8, 20, 0, 18, 12, 28, 0, 30, 16, 20, 0, 24, 12, 36, 0, 24, 16, 40, 0, 42, 20, 24, 0, 46, 16, 42, 0, 32, 24, 52, 0, 40, 24, 36, 0, 58, 16, 60, 0, 36, 32, 48, 0, 66, 32, 44, 0, 70, 24, 72, 0, 40, 36, 60, 0, 78, 32
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OFFSET
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1,3
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COMMENTS
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a(A016825(n)) = 0; a(A000040(n)) = A000040(n) - 1. - Reinhard Zumkeller, Jun 11 2012
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = if n mod 4 = 2 then 0 else A000010(n). - Reinhard Zumkeller, Jun 13 2012
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PROG
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(PARI) {for(n=1, 81, f=factor(n); print1(if(n==1, 1, if(f[1, 1]==2&&f[1, 2]==1, 0, prod(j=1, matsize(f)[1], eulerphi(f[j, 1]^f[j, 2])))), ", "))}
(Haskell)
a080736 n = if n `mod` 4 == 2 then 0 else a000010 n
-- Reinhard Zumkeller, Jun 13 2012, Jun 11 2012
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CROSSREFS
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Cf. A080737.
Cf. A000010, A141809.
Sequence in context: A127786 A030207 A061006 * A326127 A276151 A144412
Adjacent sequences: A080733 A080734 A080735 * A080737 A080738 A080739
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KEYWORD
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nonn,easy,mult
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AUTHOR
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N. J. A. Sloane, Mar 08 2003
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EXTENSIONS
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More terms and PARI code from Klaus Brockhaus, Mar 10 2003
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STATUS
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approved
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