A386010 Numbers z such that there exist two integers 0

120, 672, 1188, 1740, 2556, 11172, 11556, 11628, 27312, 32136, 41412, 41952, 42168

Offset: 1

Author

S. I. Dimitrov, Jul 14 2025

Keywords

• nonn
• hard
• more

Comments

The numbers x, y and z form a GM-amicable triple (GM = Geometric Mean). See Dimitrov link. An amicable triple forms a GM-amicable triple, so the larger member of an amicable triple A125492 is a term of this sequence.

Examples

			(1080, 1092, 1188) is such a triple because sigma(1080)*sigma(1092)*sigma(1188) = (1080 + 1092 + 1188)^3.
		

Links

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

Crossrefs

Cf. A000203, A125492, A383932.