A384411 Pairs (k, m) such that k = sigma(m) - m and m = sigma(2*k) - 2*k.

26, 46, 296, 586

Offset: 1

Author

S. I. Dimitrov, Jun 01 2025

Keywords

• nonn
• hard
• more

Comments

Fixed points of x->A346878(A001065(x)).

Next term > 15*10^7.

Examples

			(26, 46) is such a pair because 26 = sigma(46) - 46 and 46 = sigma(52) - 52.
(296, 586) is another pair.
		

Links

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

Crossrefs

Cf. A000203, A001065, A063990, A259180, A346878, A383483.

Programs

PARI

for(k=1,10^9, m = sigma(2*k) - 2*k;if(k == sigma(m) - m, print1(k, ", ", m, ", "))); \\ Joerg Arndt, Jun 01 2025