A133438 a(1)=1. a(n) = Sum_{k|n} a(floor(sqrt(k))).

1, 2, 2, 4, 3, 5, 3, 6, 4, 6, 3, 9, 3, 6, 6, 10, 5, 11, 5, 12, 8, 8, 5, 15, 6, 7, 7, 11, 4, 14, 4, 13, 7, 9, 8, 20, 6, 11, 9, 19, 6, 18, 6, 15, 13, 11, 6, 24, 6, 12, 9, 12, 4, 17, 8, 16, 9, 8, 4, 25, 4, 8, 13, 19, 11, 20, 7, 17, 12, 19, 7, 32, 7, 13, 15, 19, 11, 21, 7, 29, 11, 11, 5, 29, 11, 11, 9

Offset

1,2

Links

Table of n, a(n) for n=1..87.

Example

The divisors of 12 are 1,2,3,4,6,12. The floor of the square roots of these are 1,1,1,2,2,3. So a(12) = a(1) + a(1) + a(1) + a(2) + a(2) + a(3) = 1 + 1 + 1 + 2 + 2 + 2 = 9.

Maple

A133438 := proc(n) option remember ; local a, d; if n = 1 then 1; else a := 0 ; for d in numtheory[divisors](n) do a := a+ procnamefloor(sqrt(d))) ; od: RETURN(a) ; fi ; end:
seq(A133438(n), n=1..60) ; # R. J. Mathar, Jan 08 2008

Crossrefs

Sequence in context: A125185 A274895 A173387 * A086671 A269502 A054346

Adjacent sequences: A133435 A133436 A133437 * A133439 A133440 A133441

Keyword

nonn

Author

Leroy Quet, Nov 26 2007

Extensions

More terms from R. J. Mathar and Matthew Conroy, Jan 08 2008

Status

approved