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A209291
Sum of the refactorable numbers less than or equal to n.
1
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, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 110, 110, 110, 110, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 150, 206, 206, 206, 206, 266
OFFSET
1,2
COMMENTS
A number is refactorable if it is divisible by the number of its divisors.
The first 8 terms are odd. The next odd term after 11 is a(225) = 2395.
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
LINKS
Eric Weisstein's World of Mathematics, Refactorable Number
FORMULA
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).
MAPLE
with(numtheory); a:= n -> add(i * (1 + floor(i/tau(i)) - ceil(i/tau(i))), i = 1..n):
MATHEMATICA
Accumulate[Table[If[Divisible[n, DivisorSigma[0, n]], n, 0], {n, 60}]] (* Harvey P. Dale, Aug 07 2019 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 16 2013
STATUS
approved