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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 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.)