A383483 Numbers k such that k = sigma(m)-m where m = sigma(3*k)-3*k.

3, 15, 5919, 118719, 179871, 33750303

Offset: 1

Author

S. I. Dimitrov, Apr 28 2025

Keywords

• nonn
• more

Comments

S. I. Dimitrov introduced the notion of (alpha, beta)-amicable pairs.

Examples

			For alpha=1, beta=3 we have (3, 4), (15, 33), (5919, 7905).
Here (3, 4) is such a pair because 3=sigma(4)-4 and 4=sigma(3*3)-3*3.
		

Links

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

Crossrefs

Cf. A063990, A259180, A383239.

Programs

PARI

isok(k) = my(m = sigma(3*k) - 3*k); if (m>0, sigma(m) - m == k); \\ Michel Marcus, Apr 28 2025

Formula

We say that the numbers m and n form an (alpha, beta)-amicable pair if sigma(alpha*n)-alpha*n=m and sigma(beta*m)-beta*m=n, where alpha and beta are positive integers, and sigma(n) is the sum of the divisors of n.

Extensions

a(4)-a(6) from Michel Marcus, Apr 28 2025