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

1,2

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Project Euler, Problem 484: Arithmetic Derivative

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 *)

Prog

(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
(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

Crossrefs

Cf. A003415, A085731.

Sequence in context: A047361 A037461 A284514 * A249587 A007607 A370902

Adjacent sequences: A268395 A268396 A268397 * A268399 A268400 A268401

Keyword

nonn

Author

Peter Kagey, Feb 03 2016

Status

approved