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Arithmetic derivative of Euler's totient function phi(n).

+0
2

0, 0, 1, 1, 4, 1, 5, 4, 5, 4, 7, 4, 16, 5, 12, 12, 32, 5, 21, 12, 16, 7, 13, 12, 24, 16, 21, 16, 32, 12, 31, 32, 24, 32, 44, 16, 60, 21, 44, 32, 68, 16, 41, 24, 44, 13, 25, 32, 41, 24, 80, 44, 56, 21, 68, 44, 60, 32, 31, 32, 92, 31, 60, 80, 112, 24, 61, 80, 48, 44, 59, 44, 156, 60 (list; graph; listen)

	OFFSET	`1,5`
	REFERENCES	`See A003415`
	FORMULA	`a(n) = A003415(A000010(n))`
	MATHEMATICA	`dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Table[dn[EulerPhi[n]], {n, 100}]`
	CROSSREFS	`Cf. A003415 (arithmetic derivative of n).` `Sequence in context: A030352 A104571 A105721 this_sequence A021880 A075013 A117379` `Adjacent sequences: A099307 A099308 A099309 this_sequence A099311 A099312 A099313`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Oct 12 2004`

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.

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