A383964 -id:A383964 - cp's OEIS frontend

A384487 Numbers k such that there exist two integers 0

396, 504, 600, 756, 840, 924, 1056, 1080, 1140, 1170, 1260, 1320, 1428, 1440, 1488, 1512, 1540, 1560, 1596, 1638, 1650, 1656, 1680, 1704, 1710, 1740, 1800, 1820, 1840, 1848, 1872, 1932, 1980, 2016, 2040, 2100, 2160, 2184, 2232, 2244, 2256, 2280, 2340, 2352, 2380, 2400, 2430, 2436, 2448, 2460, 2484

Offset: 1

S. I. Dimitrov, Jun 01 2025

nonn

The numbers i, j and k form a WHM(1)-amicable triple (WHM = weighted harmonic mean). See Dimitrov link.

			504 is a term because (72, 360, 504) is a triple with 72/sigma(72) + 360/sigma(360) + 504/sigma(504) = 1.
420 is not a term because the corresponding triple is (84, 420, 420).

Robert Israel, Table of n, a(n) for n = 1..600
S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Cf. A000203, A125490, A125491, A125492, A253534, A253535, A383964.

S:= {}: S2:= {}: R:= NULL: count:= 0:
for k from 1 while count < 100 do
  v:= k/numtheory:-sigma(k);
  if member(1-v,S2) then
    R:= R, k; count:= count+1;
 fi;
  S2:= S2 union map(t -> `if`(t+v<1,t+v,NULL),S);
  S:= S union {v};
od:
R; # Robert Israel, Jul 01 2025

isok(k) = for (i=1, k-1, for (j=i+1, k-1, if (i/sigma(i) + j/sigma(j) + k/sigma(k) == 1, /* print([i,j,k]); */ return(1)););); \\ Michel Marcus, Jun 02 2025

More terms from Michel Marcus, Jun 02 2025

A384814 Integers k such that there exists an integer 0

Original entry on oeis.org

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

S. I. Dimitrov, Jun 10 2025

nonn

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.

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

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

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

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

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

cp's OEIS Frontend

A384487 Numbers k such that there exist two integers 0

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