A268398 Partial sums of A085731.

1, 2, 3, 7, 8, 9, 10, 14, 17, 18, 19, 23, 24, 25, 26, 42, 43, 46, 47, 51, 52, 53, 54, 58, 63, 64, 91, 95, 96, 97, 98, 114, 115, 116, 117, 129, 130, 131, 132, 136, 137, 138, 139, 143, 146, 147, 148, 164, 171, 176, 177, 181, 182, 209, 210, 214, 215, 216, 217

Offset: 1

Author

Peter Kagey, Feb 03 2016

Keywords

• nonn

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• Project Euler, Problem 484: Arithmetic Derivative

Crossrefs

Cf. A003415, A085731.

Programs

Mathematica

Accumulate@ Table[GCD[n, If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]], {n, 58}] (* Michael De Vlieger, Feb 14 2016, after Michael Somos at A003415  *)
Accumulate@ Table[GCD[n, If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]], {n, 58}] (* Michael De Vlieger, Feb 14 2016 *)

PARI

a085731(n) = {my(f = factor(n)); for (i=1, #f~, if (f[i,2] % f[i,1], f[i,2]--);); factorback(f);}
a(n) = sum(k=1, n, a085731(k)); \\ Michel Marcus, Feb 14 2016

Ruby

require 'prime'
def a003415(n)
  return 0 if n == 1
  return 1 if Prime.prime?(n)
  a = Prime.each.find { |i| n % i == 0 }
  a * a003415(n/a) + n/a * a003415(a)
end
def a268398(n)
  sum = 0
  (1..n).map { |n| sum += a003415(n).gcd(n) }.last
end