A068981 Arithmetic derivative of n*prime(n).

1, 5, 8, 32, 16, 71, 24, 236, 147, 213, 42, 604, 54, 401, 391, 1712, 76, 1299, 86, 1724, 751, 1049, 106, 3940, 995, 1541, 2808, 3452, 138, 3533, 158, 10512, 1951, 2675, 1823, 9096, 194, 3461, 2711, 11804, 220, 7463, 234, 9308, 7728, 5021, 258, 25024, 3227, 10355

Offset: 1

Author

Reinhard Zumkeller, Apr 01 2002

Keywords

• nonn
• easy

Examples

			a(10) = A003415(A033286(10)) = A003415(A000040(10)*10) = A003415(29*10) = A003415(29)*10 + 29*A003415(10) = 1*10 + 29*(2*1 + 1*5) = 10 + 29*7 = 213.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A003415, A033286.

Programs

Mathematica

a[n_] := n * Prime[n] * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n*Prime[n]]); Array[a, 100] (* Amiram Eldar, May 17 2025 *)

Formula

a(n) = n + A000040(n)*A003415(n).

a(n) = A003415(A033286(n)) = A003415(n*A000040(n)).