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

26, 46, 296, 586

Offset

1,1

Comments

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

Next term > 15*10^7.

Links

Table of n, a(n) for n=1..4.

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A255988 A304673 A039458 * A291672 A159651 A118367

Adjacent sequences: A384408 A384409 A384410 * A384412 A384413 A384414

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Jun 01 2025

Status

approved