cp's OEIS Frontend

A209291 Sum of the refactorable numbers less than or equal to n.

%I A209291 #28 Feb 16 2025 08:33:16
%S A209291 1,3,3,3,3,3,3,11,20,20,20,32,32,32,32,32,32,50,50,50,50,50,50,74,74,
%T A209291 74,74,74,74,74,74,74,74,74,74,110,110,110,110,150,150,150,150,150,
%U A209291 150,150,150,150,150,150,150,150,150,150,150,206,206,206,206,266
%N A209291 Sum of the refactorable numbers less than or equal to n.
%C A209291 A number is refactorable if it is divisible by the number of its divisors.
%C A209291 The first 8 terms are odd. The next odd term after 11 is a(225) = 2395.
%C A209291 600 out of the first 1000 terms are odd, including every term from a(625) up to and including a(1000). - _Harvey P. Dale_, Aug 07 2019
%H A209291 Harvey P. Dale, <a href="/A209291/b209291.txt">Table of n, a(n) for n = 1..1000</a>
%H A209291 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RefactorableNumber.html">Refactorable Number</a>
%F A209291 a(n) = Sum_{i=1..n} i*(1 + floor(i/d(i)) - ceiling(i/d(i))) where d(n) is the number of divisors of n (A000005).
%p A209291 with(numtheory); a:= n -> add(i * (1 + floor(i/tau(i)) - ceil(i/tau(i))), i = 1..n):
%t A209291 Accumulate[Table[If[Divisible[n,DivisorSigma[0,n]],n,0],{n,60}]] (* _Harvey P. Dale_, Aug 07 2019 *)
%Y A209291 Cf. A033950, A000005, A141586, A057265, A036896, A036898, A114617.
%K A209291 nonn
%O A209291 1,2
%A A209291 _Wesley Ivan Hurt_, Jan 16 2013