A078323 Arithmetic derivative of n*rad(n)+1, where rad = A007947 (squarefree kernel).

1, 1, 7, 6, 15, 1, 45, 1, 32, 1, 63, 1, 129, 1, 115, 14, 213, 1, 183, 70, 281, 102, 381, 34, 165, 1, 43, 134, 423, 70, 581, 18, 773, 102, 615, 38, 969, 459, 763, 1, 957, 358, 1715, 431, 780, 102, 1847, 34, 524, 170, 1303, 607, 1977, 155, 1725, 162, 3825, 678, 1743

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2002

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A007947 (rad), A078310, A078322.

Programs

Haskell

a078323 = a003415 . a078310  -- Reinhard Zumkeller, Jul 23 2013

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := ad[1 + n * Times @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* Amiram Eldar, Apr 10 2025 *)

Formula

a(n) = A003415(A078310(n)).