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A239930 Number of distinct quarter-squares dividing n. 4
1, 2, 1, 3, 1, 3, 1, 3, 2, 2, 1, 5, 1, 2, 1, 4, 1, 4, 1, 4, 1, 2, 1, 5, 2, 2, 2, 3, 1, 4, 1, 4, 1, 2, 1, 7, 1, 2, 1, 4, 1, 4, 1, 3, 2, 2, 1, 6, 2, 3, 1, 3, 1, 4, 1, 4, 1, 2, 1, 7, 1, 2, 2, 5, 1, 3, 1, 3, 1, 2, 1, 8, 1, 2, 2, 3, 1, 3, 1, 5, 3, 2, 1, 6, 1, 2, 1, 3, 1, 6, 1, 3, 1, 2, 1, 6, 1, 3, 2, 6, 1, 3, 1, 3, 1, 2, 1, 7, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For more information about the quarter-squares see A002620.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Wikipedia, Table of divisors

FORMULA

a(n) = Sum_{k=1..A000005(n)} A240025(A027750(n,k)). - Reinhard Zumkeller, Jul 05 2014

EXAMPLE

For n = 12 the quarter-squares <= 12 are [0, 0, 1, 2, 4, 6, 9, 12]. There are five quarter-squares that divide 12; they are [1, 2, 4, 6, 12], so a(12) = 5.

MAPLE

isA002620 := proc(n)

    local k, qsq ;

    for k from 0 do

        qsq := floor(k^2/4) ;

        if n = qsq then

            return true;

        elif qsq > n then

            return false;

        end if;

    end do:

end proc:

A239930 := proc(n)

    local a, d ;

    a :=0 ;

    for d in numtheory[divisors](n) do

        if isA002620(d) then

            a:= a+1 ;

        end if;

    end do:

    a;

end proc: # R. J. Mathar, Jul 03 2014

MATHEMATICA

qsQ[n_] := AnyTrue[Range[Ceiling[2 Sqrt[n]]], n == Floor[#^2/4]&]; a[n_] := DivisorSum[n, Boole[qsQ[#]]&]; Array[a, 110] (* Jean-Fran├žois Alcover, Feb 12 2018 *)

PROG

(Haskell)

a239930 = sum . map a240025 . a027750_row

-- Reinhard Zumkeller, Jul 05 2014

CROSSREFS

Cf. A000005, A001221, A001511, A002620, A005086, A006519, A007862, A027750, A046951, A147645, A236103.

Cf. A240025.

Sequence in context: A029242 A029236 A152188 * A226859 A025820 A109704

Adjacent sequences:  A239927 A239928 A239929 * A239931 A239932 A239933

KEYWORD

nonn

AUTHOR

Omar E. Pol, Jun 19 2014

STATUS

approved

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Last modified April 10 16:05 EDT 2021. Contains 342845 sequences. (Running on oeis4.)