A384814 Integers k such that there exists an integer 0

28, 56, 66, 88, 90, 114, 132, 174, 220, 234, 238, 246, 284, 306, 308, 312, 340, 348, 356, 496, 532, 534, 552, 618, 620, 654, 668, 728, 752, 760, 786, 812, 856, 963, 990, 992, 996, 1052, 1092, 1148, 1180, 1196, 1210, 1220, 1232, 1244, 1288, 1320, 1326, 1364, 1372, 1474, 1494, 1580

Offset: 1

Author

S. I. Dimitrov, Jun 10 2025

Keywords

• nonn

Comments

The numbers m and k form a HM(1,2)-amicable pair (HM = harmonic mean). See Dimitrov link. An amicable pair forms a HM(1,2)-amicable pair, so the larger member of an amicable pair A002046 is a term of this sequence.

Examples

			(20, 28) is such a pair because (1/sigma(20) + 1/sigma(28))*(20+28) = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..250
• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Cf. A000203, A000396, A002025, A002046, A383964.

Programs

Maple

S:= map(numtheory:-sigma,[$1..3000]):
filter:= proc(k)
   ormap(m -> (1/S[m] + 1/S[k])*(m+k) = 2, [$1..k-1])
end proc:
select(filter, [$1..3000]); # Robert Israel, Jul 25 2025

PARI

isok(k) = for(m=1, k-1, if ((1/sigma(m) + 1/sigma(k))*(m+k) == 2, return(1))); \\ Michel Marcus, Jun 10 2025