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A216157
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Difference between the sum of the even divisors and the sum of the odd divisors of phi(n).
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1
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1, 1, 5, 1, 4, 5, 4, 5, 6, 5, 20, 4, 13, 13, 29, 4, 13, 13, 20, 6, 12, 13, 30, 20, 13, 20, 40, 13, 24, 29, 30, 29, 52, 20, 65, 13, 52, 29, 78, 20, 32, 30, 52, 12, 24, 29, 32, 30, 61, 52, 70, 13, 78, 52, 65, 40, 30, 29, 120, 24, 65, 61, 116, 30, 48, 61, 60, 52
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OFFSET
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3,3
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COMMENTS
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phi(n) : A000010 is the Euler totient function, and even for n > 2.
If n prime, phi(n) = n-1 and a(n) = a((n-1)/2).
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LINKS
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EXAMPLE
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a(13) = 20 because the divisors of phi(13) = 12 are {1, 2, 3, 4, 6, 12} and (12 + 6 + 4 +2) - (3 + 1) = 20.
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MAPLE
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with(numtheory):for n from 3 to 100 do:x:=divisors(phi(n)):n1:=nops(x):s0:=0:s1:=0:for m from 1 to n1 do: if irem(x[m], 2)=0 then s0:=s0+x[m]:else s1:=s1+x[m]:fi:od:if s0>s1 then printf(`%d, `, s0-s1):else fi:od:
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MATHEMATICA
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Table[Total[Select[Divisors[EulerPhi[n]], EvenQ[#]&]]-Total[Select[Divisors[EulerPhi[n]], OddQ[#]&]], {n, 3, 80}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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