A383964 Integers k such that there exists an integer 0

168, 1320, 3792, 4968, 7176, 8184, 14364, 15240, 20076, 29904, 30672, 41952, 48312, 48768, 54264, 56856, 57960, 60144, 64296, 72996, 73344, 83328, 90552, 91512, 99828, 106020, 110952, 113280, 114156, 119016, 128592, 149292, 150024, 151272, 157608, 168588, 175584, 183240

Offset: 1

Author

S. I. Dimitrov, May 16 2025

Keywords

• nonn

Comments

The numbers m and k form a HM(2,1)-amicable pair (HM = harmonic mean). See Dimitrov link.

Examples

			(120, 168) is such a pair because (1/sigma(120)^2 + 1/sigma(168)^2)*(120+168)^2 = 1.
		

Links

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

Crossrefs

Cf. A063990, A259180, A383239, A383483, A383484.

Programs

PARI

isok(k) = for(m=1, k-1, if((1/sigma(m)^2 + 1/sigma(k)^2)*(m+k)^2 == 1, return(m))); \\ Michel Marcus, May 16 2025

Extensions

a(7) and a(9)-a(25) from Michel Marcus, May 16 2025

More terms from David A. Corneth, Jun 21 2025