A385749 Numbers z such that there exist two integers 0

120, 672, 1740, 2556, 4680, 11556, 27312, 32136, 41412, 41952, 42168

Offset: 1

Author

S. I. Dimitrov, Jul 08 2025

Keywords

• nonn
• hard
• more

Comments

The numbers x, y and z form a WHM(2)-amicable triple (WHM = weighted harmonic mean). An amicable triple forms a WHM(2)-amicable triple, so the larger member of an amicable triple A125492 is a term of this sequence.

Examples

			(1980, 2016, 2556) is such a triple because (1980^2/sigma(1980)^2 + 2016^2/sigma(2016)^2 + 2556^2/sigma(2556)^2)*(1980 + 2016 + 2556)^2 = 1980^2 + 2016^2 + 2556^2.
Other kinds of triples are: (120,120,120), (1560, 1740, 1740) and (117, 117, 4680).
Note that (117, 117, 4680) is the only known WHM(2)-amicable triple that is not an amicable triple.
		

Links

• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Cf. A000203, A125492, A384487.

Cf. A005820 (a subsequence, for (x,x,x) triples).