A383714 Integers k such that there exists an integer 0

21, 231, 284, 1210, 2499, 2924, 5564, 6368, 10856, 14595, 18416, 66992, 71145, 76084, 87633, 88730

Offset: 1

Author

S. I. Dimitrov, May 14 2025

Keywords

• nonn
• more

Comments

The numbers m and k form a WPM(2)-amicable pair (WPM = weighted power mean). See Dimitrov link.

Examples

			(7, 21) is such a pair because 7*sigma(7)^2 + 21*sigma(21)^2 = 7*8^2 + 21*32^2 = (7+21)^3.
		

Links

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

Crossrefs

Cf. A002046 (a subsequence), A063990, A259180, A383239, A383483, A383484.

Programs

PARI

isok(k)= for (m=1, k-1, if (m*sigma(m)^2 + k*sigma(k)^2 == (m+k)^3, return(m))); \\ Michel Marcus, May 15 2025

Extensions

a(3)-a(16) from Michel Marcus, May 15 2025