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

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

Author

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

Keywords

• nonn

Comments

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

Examples

			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).
		

Links

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

Crossrefs

Cf. A321490, A321491.

Programs

PARI

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