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

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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 *)

Crossrefs

Cf. A033950, A000005, A141586, A057265, A036896, A036898, A114617.

Sequence in context: A105159 A365458 A334625 * A375642 A332875 A176873

Adjacent sequences: A209288 A209289 A209290 * A209292 A209293 A209294

Keyword

nonn

Author

Wesley Ivan Hurt, Jan 16 2013

Status

approved