id:A099306 - OEIS Search Results

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n''', the third arithmetic derivative of n.

+0
3

0, 0, 0, 4, 0, 0, 0, 32, 1, 0, 0, 80, 0, 5, 16, 176, 0, 7, 0, 48, 1, 0, 0, 112, 1, 12, 27, 176, 0, 0, 0, 368, 6, 0, 32, 96, 0, 7, 80, 156, 0, 0, 0, 240, 32, 7, 0, 608, 6, 16, 44, 96, 0, 216, 80, 272, 1, 0, 0, 272, 0, 9, 24, 2368, 10, 0, 0, 220, 8, 0, 0, 284, 0, 32, 32, 368, 10, 0, 0, 752 (list; graph; listen)

	OFFSET	`1,4`
	COMMENT	`For prime p, a(p^p) = p^p.`
	REFERENCES	`See A003415`
	FORMULA	`a(n) = A003415(A003415(A003415(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[dn[dn[n]]], {n, 100}]`
	CROSSREFS	`Cf. A003415 (arithmetic derivative of n), A068346 (second arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero).` `Sequence in context: A074037 A126849 A057386 this_sequence A101193 A013334 A096623` `Adjacent sequences: A099303 A099304 A099305 this_sequence A099307 A099308 A099309`
	KEYWORD	`nonn`
	AUTHOR	`T. D. Noe (noe(AT)sspectra.com), Oct 12 2004`

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Last modified September 8 08:06 EDT 2008. Contains 143486 sequences.

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