id:A068328 - OEIS Search Results

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Arithmetic derivative of square-free numbers.

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4

0, 1, 1, 1, 5, 1, 7, 1, 1, 9, 8, 1, 1, 10, 13, 1, 15, 1, 31, 1, 14, 19, 12, 1, 21, 16, 1, 41, 1, 25, 1, 20, 1, 16, 22, 31, 1, 1, 33, 18, 61, 1, 26, 59, 1, 1, 39, 18, 71, 1, 43, 1, 22, 45, 32, 1, 20, 34, 49, 24, 1, 1, 91, 1, 71, 55, 1, 1, 87, 40, 1, 101, 28, 61, 24, 63, 44, 1, 46 (list; graph; listen)

	OFFSET	`1,5`
	COMMENT	`a(n) = A003415(A005117(n)).` `a(n) = A069359(A005117(n)).`
	FORMULA	`a(n) = Sum(A005117(n)/p: prime p divides A005117(n)).`
	EXAMPLE	`a(65) = d(A005117(65)) = d(105) = d(335) = 3d(35)+d(3)35 = 3d(57)+135 = 3d(57)+135 = 3(5d(7)+d(5)7)+35 = 3(51+17)+35 = 312+35 = 71, where d(n) = A003415(n)` `with d(1)=0, d(prime)=1 and d(mn)=d(m)n+m*d(n).`
	CROSSREFS	`Sequence in context: A111008 A065330 A140215 this_sequence A109375 A051712 A086892` `Adjacent sequences: A068325 A068326 A068327 this_sequence A068329 A068330 A068331`
	KEYWORD	`nonn`
	AUTHOR	`Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 27 2002`

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Last modified November 30 13:13 EST 2009. Contains 167758 sequences.

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