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A110173
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Least k such that phi(n) = phi(k) + phi(n-k) for 0<k<n, or 0 if there is no such k, where phi is Euler's totient function.
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5
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0, 0, 1, 2, 0, 0, 0, 4, 4, 4, 0, 6, 0, 4, 5, 8, 0, 6, 0, 6, 5, 6, 0, 6, 6, 4, 11, 6, 0, 0, 0, 16, 6, 8, 10, 12, 0, 4, 13, 12, 0, 12, 0, 6, 7, 8, 0, 12, 0, 10, 16, 6, 0, 6, 26, 12, 19, 26, 0, 30, 0, 4, 12, 32, 24, 24, 0, 6, 23, 28, 0, 18, 0, 10, 12, 8, 24, 12, 0, 24, 0, 8, 0, 24, 8, 4, 6, 12, 0, 30
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OFFSET
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1,4
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COMMENTS
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Sequence A110174 gives the number of solutions 0<k<n. Note that a(n)=0 for all primes except 3. It is also zero for the composite numbers in A110175.
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LINKS
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MATHEMATICA
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a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]
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PROG
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(PARI) A110173(n) = { my(ph=eulerphi(n)); for(k=1, n-1, if(ph == (eulerphi(k)+eulerphi(n-k)), return(k))); (0); }; \\ Antti Karttunen, Feb 20 2023
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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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