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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..51.

Example

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.

Prog

(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}

Crossrefs

Cf. A321490, A321492.

Sequence in context: A223432 A044092 A044473 * A067724 A005337 A160891

Adjacent sequences: A321488 A321489 A321490 * A321492 A321493 A321494

Keyword

nonn

Author

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

Status

approved