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A057373 Numbers k that can be expressed as k = w + x = y*z with w*x = y^2 + z^2 where w, x, y, and z are all positive integers. 5
9, 18, 45, 90, 117, 306, 522, 585, 801, 1305, 2097, 3042, 3978, 5490, 8730, 14373, 17730, 19485, 22698, 27234, 37629, 44109, 98514, 103338, 113013, 130365, 155025, 186633, 257913, 290970, 405450, 602298, 675225, 884637, 1279170, 1498185, 1767762, 1946745 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Robert Israel, Feb 01 2016: (Start)

Numbers k such that k^2 - 4*(d^2 + k^2/d^2) is a square for some divisor d of k.

All terms are divisible by 9.

Includes 9*A001519(k) for all k (where y = 3, z = 3*A001519(k)). In particular, the sequence is infinite. (End)

LINKS

Table of n, a(n) for n=1..38.

MAPLE

filter:= proc(n) local x;

  nops(select(x -> issqr(n^2-4*x^2 - 4*(n/x)^2), numtheory:-divisors(n)))>0;

end proc:

select(filter, [$1..10^6]); # Robert Israel, Feb 01 2016

PROG

(PARI) is(k) = fordiv(k, y, if(issquare(k^2 - 4*y^2 - 4*sqr(k/y)), return(1))); 0; \\ Jinyuan Wang, May 02 2021

CROSSREFS

Cf. A001519, A057369, A057370, A057371, A057372, A057444.

Sequence in context: A000547 A138900 A202187 * A153185 A325450 A212345

Adjacent sequences:  A057370 A057371 A057372 * A057374 A057375 A057376

KEYWORD

nonn

AUTHOR

Naohiro Nomoto, Sep 24 2000

EXTENSIONS

a(19)-a(38) from Robert Israel, Feb 01 2016

New name from Jinyuan Wang, May 02 2021

STATUS

approved

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)