id:A110173 - OEIS Search Results

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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 k, where phi is Euler's totient function.

+0
4

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 (list; graph; listen)

	OFFSET	`1,4`
	COMMENT	`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.`
	MATHEMATICA	`a[n_] := Select[Range[n-1], EulerPhi[n]==EulerPhi[n-# ]+EulerPhi[ # ]&]; Table[s=a[n]; If[Length[s]==0, 0, First[s]], {n, 150}]`
	CROSSREFS	`Cf. A066426 (least k such that phi(n)+phi(k)=phi(n+k)).` `Sequence in context: A100951 A011991 A129183 this_sequence A131427 A113044 A051883` `Adjacent sequences: A110170 A110171 A110172 this_sequence A110174 A110175 A110176`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Jul 15 2005`

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Last modified July 26 23:19 EDT 2008. Contains 142293 sequences.

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