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A175497 Numbers n with property that n^2 is a product of two distinct triangular numbers. 3
0, 6, 30, 35, 84, 180, 204, 210, 297, 330, 546, 840, 1170, 1189, 1224, 1710, 2310, 2940, 2970, 3036, 3230, 3900, 4914, 6090, 6930, 7134, 7140, 7245, 7440, 8976, 10710, 12654, 14175, 14820, 16296, 16380, 17220, 19866, 22770, 25172, 25944, 29103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Contribution from Robert G. Wilson v, Jul 24 2010: (Start)

1) 0, 6, 35, 204, 1189, 6930, 40391, 235416, 1372105, 7997214, 46611179,...

2) 30, 297, 2940, 29103, 288090, 2851797, 28229880,...

3) 84, 1170, 16296, 226974, 3161340,...

4) 180, 3230, 57960, 1040050, 18662940,..

5) 330, 7245, 159060, 3492075, 76666590,...

6) 546, 14175, 368004, 9553929,...

7) 840, 25172, 754320, 22604428,...

8) 210, 1224, 7134, 41580, 242346, 1412496, 8232630, 47983284,...

9) 1710, 64935, 2465820, 93636225,...

10) 2310, 96965, 4070220,...

11) 3036, 139590, 6418104,...

12) 3900, 194922, 9742200,...

13) 4914, 265265, 14319396,...

14) 6090, 353115, 20474580,...

15) 7440, 461160, 28584480,...

(End)

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..427 . [From Robert G. Wilson v, Jul 24 2010]

MAPLE

isA175497 := proc(n)

    local i, Ti, Tj;

    if n = 0 then

        return true;

    end if;

    for i from 1 do

        Ti := i*(i+1)/2 ;

        if Ti > n^2 then

            return false;

        else

            Tj := n^2/Ti ;

            if Tj <> Ti and type(Tj, 'integer') then

                if isA000218(Tj) then  # code in A000218

                    return true;

                end if;

            end if;

        end if;

    end do:

end proc:

for n from 0 do

    if isA175497(n) then

        printf("%d, \n", n);

    end if;

end do: # R. J. Mathar, May 26 2016

MATHEMATICA

m = 30000; lst = {0}; Do[r = n (n + 1)/2; Do[s = Sqrt[r*t[k]]; If[IntegerQ@s, AppendTo[lst, s]; Print[{n, k, s}]], {k, n + 1, Sqrt[2 m (m - 1)/r]}], {n, 3 m^(1/4)}]; Union@lst

CROSSREFS

Contribution from Robert G. Wilson v, Jul 24 2010: (Start)

A001109(with the exception of 1), A011945, A075848 & A055112 are all proper subsets.

Many terms are in common with A147779.

Cf. A001108, A132596, A007654, A001108, A132593. (End)

Sequence in context: A068510 A147798 A197880 * A161812 A282944 A188062

Adjacent sequences:  A175494 A175495 A175496 * A175498 A175499 A175500

KEYWORD

nonn

AUTHOR

Zak Seidov, May 30 2010

EXTENSIONS

I redid the Mathematica coding, changed the offset from (0,2) to (1,2) and took out the Comment line about more terms and will submit a b text file Robert G. Wilson v, Jul 22 2010

STATUS

approved

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Last modified August 19 20:20 EDT 2019. Contains 326133 sequences. (Running on oeis4.)