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A280712
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Inverse Euler transform of A280611.
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4
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2, 1, 0, 1, 0, 4, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 4, 0, 3, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 0, 7, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 9, 0, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 1, 0
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OFFSET
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1,1
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COMMENTS
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a(n) = b(n) for n odd, a(n) = b(n) - b(n/2) for n even >= 2, where b(n) = A014197(n) = the number of m with phi(m) = n.
Note that a(n) = 0 for all odd n > 1, and so a(n) = b(n) for n >= 3, n not a multiple of 4.
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LINKS
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FORMULA
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Euler transform of sequence = Product_{k>=1} (1-x^k)^(-a(k)) is the g.f. of A280611.
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EXAMPLE
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a(4) = #{m:phi(m) = 4} - #{m:phi(m) = 2} = #{5,8,10,12} - #{2,4,6} = 4-3 = 1.
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PROG
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(PARI)
A014197(n, m=1) = { n==1 && return(1+(m<2)); my(p, q); sumdiv(n, d, if( d>=m && isprime(d+1), sum( i=0, valuation(q=n\d, p=d+1), A014197(q\p^i, p))))}; \\ From A014197
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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