cp's OEIS Frontend

A268398 Partial sums of A085731.

%I A268398 #17 Feb 14 2016 14:37:39
%S A268398 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,
%T A268398 64,91,95,96,97,98,114,115,116,117,129,130,131,132,136,137,138,139,
%U A268398 143,146,147,148,164,171,176,177,181,182,209,210,214,215,216,217
%N A268398 Partial sums of A085731.
%H A268398 Peter Kagey, <a href="/A268398/b268398.txt">Table of n, a(n) for n = 1..10000</a>
%H A268398 Project Euler, <a href="https://projecteuler.net/problem=484">Problem 484: Arithmetic Derivative</a>
%t A268398 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  *)
%t A268398 Accumulate@ Table[GCD[n, If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger@ Abs@ n]]], {n, 58}] (* _Michael De Vlieger_, Feb 14 2016 *)
%o A268398 (Ruby)
%o A268398 require 'prime'
%o A268398 def a003415(n)
%o A268398   return 0 if n == 1
%o A268398   return 1 if Prime.prime?(n)
%o A268398   a = Prime.each.find { |i| n % i == 0 }
%o A268398   a * a003415(n/a) + n/a * a003415(a)
%o A268398 end
%o A268398 def a268398(n)
%o A268398   sum = 0
%o A268398   (1..n).map { |n| sum += a003415(n).gcd(n) }.last
%o A268398 end
%o A268398 (PARI) a085731(n) = {my(f = factor(n)); for (i=1, #f~, if (f[i,2] % f[i,1], f[i,2]--);); factorback(f);}
%o A268398 a(n) = sum(k=1, n, a085731(k)); \\ _Michel Marcus_, Feb 14 2016
%Y A268398 Cf. A003415, A085731.
%K A268398 nonn
%O A268398 1,2
%A A268398 _Peter Kagey_, Feb 03 2016