A386010 Numbers z such that there exist two integers 0<x<=y<=z such that sigma(x)*sigma(y)*sigma(z) = (x + y + z)^3.

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

Offset

1,1

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.

Links

Table of n, a(n) for n=1..13.

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

Example

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

Crossrefs

Cf. A000203, A125492, A383932.

Sequence in context: A229568 A388026 A342923 * A385749 A292365 A388025

Adjacent sequences: A386007 A386008 A386009 * A386011 A386012 A386013

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jul 14 2025

Status

approved