A321490 -id:A321490 - cp's OEIS frontend

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

15, 40, 65, 85, 120, 156, 175, 203, 259, 272, 320, 369, 400, 405, 477, 520, 580, 585, 671, 680, 715, 803, 820, 888, 935, 960, 1080, 1105, 1111, 1157, 1248, 1261, 1400, 1417, 1464, 1484, 1624, 1625, 1695, 1755, 1820, 1875, 1885, 2055, 2072, 2080, 2176, 2295, 2336, 2380, 2465

Offset: 1

Geoffrey B. Campbell and M. F. Hasler, Nov 22 2018

nonn

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.

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

Cf. A321490, A321492.

list_A321491(L=1e4,S=[])={for(m=2, sqrtnint(L, 3), for(n=1, m-1, if(L

A321492 Numbers that can be written as (x + y)(x^2 + y^2), x > y > 0, in at least two ways.

Original entry on oeis.org

12325, 98600, 117720, 146705, 206312, 263840, 332775, 378505, 400945, 500200, 651456, 687245, 734400, 741845, 773800, 788800, 799240, 941760, 1173640, 1327360, 1533195, 1540625, 1650496, 1735105, 1836680, 1943240, 2048320, 2050880, 2110720, 2217280, 2662200, 2704360, 2965685

Offset: 1

Geoffrey B. Campbell and M. F. Hasler, Nov 22 2018

nonn

See A321491 for numbers of the form (x+y)(x^2+y^2) = A321490(x,y) with x > y > 0.

			12325 = (13+16)(13^2+16^2) = (3+22)(3^2+22^2).
98600 = (26+32)(26^2+32^2) = (6+44)(6^2+44^2).
117720 = (21+39)(21^2+39^2) = (8+46)(8^2+46^2).
146705 = (24+41)(24^2+41^2) = (14+47)(14^2+47^2).
206312 = (15+53)(15^2+53^2) = (32+42)(32^2+42^2).
263840 = (6+62)(6^2+62^2) = (33+47)(33^2+47^2).

Geoffrey B. Campbell, (m+n)(m²+n²) in two different ways, LinkedIn Number Theory Group, Aug. 2018

Cf. A321490, A321491.

A321492_list(L=1e6)={my(S=[],T=List(),t);for(m=2,sqrtn(L,3),while(#S&&S[1]<=m^3, S=S[^1]); for(n=1,m-1,if(L

cp's OEIS Frontend

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

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