A383932 Integers k such that there exists an integer 0<m<k such that sigma(m)*sigma(k) = (m+k)^2.

84, 102, 160, 186, 276, 284, 330, 582, 624, 762, 868, 1164, 1210, 1372, 1404, 1446, 1488, 1540, 1988, 2156, 2640, 2716, 2898, 2924, 3556, 3708, 3882, 4074, 4228, 4536, 5382, 5564, 5610, 5802, 6018, 6282, 6368, 6392, 6486, 6612, 6748, 7140, 7452, 7494, 7960, 8358, 8432, 9222, 9834

Offset

1,1

Comments

The numbers m and k form a GM-amicable pair. See Dimitrov link.

Links

Table of n, a(n) for n=1..49.

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

Example

For k=2 we have (28, 84), (42, 102), (60, 276), (92, 160).

Prog

(PARI) isok(k) = for (m=1, k-1, if (sigma(m)*sigma(k) == (m+k)^2, return(m))); \\ Michel Marcus, May 15 2025

Crossrefs

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

Sequence in context: A113931 A352230 A214866 * A111313 A157119 A209204

Adjacent sequences: A383929 A383930 A383931 * A383933 A383934 A383935

Keyword

nonn

Author

S. I. Dimitrov, May 15 2025

Extensions

More terms from Michel Marcus, May 15 2025

Status

approved