

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
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OFFSET

1,2


COMMENTS

A number is refactorable if it is divisible by the number of its divisors.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
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);


PROG

(PARI) a(n) = sum(i=1, n, q = i/numdiv(i); 1+ floor(q)  ceil(q)); \\ Michel Marcus, Sep 10 2018


CROSSREFS

Cf. A033950, A000005, A141586, A057265, A036896, A036898, A114617.
Partial sums of A336040.
Sequence in context: A109701 A124751 A103374 * A241087 A137722 A081305
Adjacent sequences: A208248 A208249 A208250 * A208252 A208253 A208254


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jan 12 2013


STATUS

approved



