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 A321491 Numbers of the form (x+y)(x^2+y^2), with integers x > y > 0. 4

%I #6 Nov 24 2018 01:07:29

%S 15,40,65,85,120,156,175,203,259,272,320,369,400,405,477,520,580,585,

%T 671,680,715,803,820,888,935,960,1080,1105,1111,1157,1248,1261,1400,

%U 1417,1464,1484,1624,1625,1695,1755,1820,1875,1885,2055,2072,2080,2176,2295,2336,2380,2465

%N Numbers of the form (x+y)(x^2+y^2), with integers x > y > 0.

%C If y = 0 is allowed, this adds the cubes A000578; if x = y is allowed, this adds A033430 = numbers of the form 4*x^3. None of these variants is in the OEIS yet.

%e Let f(x,y) = (x+y)(x^2+y^2) = A321490(x,y), then:

%e a(1) = f(2,1) = 3*5 = 15,a(2) = f(3,1) = 4*10 = 40, a(3) = f(3,2) = 5*13 = 65,a(4) = f(4,1) = 5*17 = 85,a(5) = f(4,2) = 6*20 = 120, etc.

%o (PARI) list_A321491(L=1e4,S=[])={for(m=2, sqrtnint(L, 3), for(n=1, m-1, if(L<t=(m+n)*(m^2+n^2), next(2), S=setunion(S, [t])))); S}

%Y Cf. A321490, A321492.

%K nonn

%O 1,1

%A Geoffrey B. Campbell and _M. F. Hasler_, Nov 22 2018

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Last modified July 15 21:59 EDT 2024. Contains 374334 sequences. (Running on oeis4.)