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A208251
Number of refactorable numbers less than or equal to n.
3
1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
OFFSET
1,2
COMMENTS
A number is refactorable if it is divisible by the number of its divisors.
LINKS
Eric Weisstein's World of Mathematics, Refactorable Number.
FORMULA
a(n) = Sum_{i=1..n} 1 + floor(i/d(i)) - ceiling(i/d(i)), where d(n) is the number of divisors of n.
EXAMPLE
a(1) = 1 since 1 is the first refactorable number, a(2) = 2 since there are two refactorable numbers less than or equal to 2, a(3) through a(7) = 2 since the next refactorable number is 8.
MAPLE
with(numtheory) a:=n->sum((1 + floor(i/tau(i)) - ceil(i/tau(i))), i=1..n);
MATHEMATICA
Accumulate[Table[If[Divisible[n, DivisorSigma[0, n]], 1, 0], {n, 1, 100}]] (* Amiram Eldar, Oct 11 2023 *)
PROG
(PARI) a(n) = sum(i=1, n, q = i/numdiv(i); 1+ floor(q) - ceil(q)); \\ Michel Marcus, Sep 10 2018
CROSSREFS
Partial sums of A336040.
Sequence in context: A109701 A124751 A103374 * A241087 A137722 A081305
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 12 2013
STATUS
approved