A383239 Integers k such that there exists an integer 0<m<k such that sigma(k) = sigma(m) = m + 2*k.

1740, 7776, 22428, 55968, 106140, 143910, 198792, 246510, 309582, 326196, 411138, 421596, 428256, 590112, 639288, 697158, 870552, 941094, 958716, 1060956, 1087776, 1105884, 1269828, 1341660, 1361568, 1447620, 1495494, 1512810, 1626324, 1727940, 1819392

Offset

1,1

Comments

S. I. Dimitrov introduced the notion of (alpha_1,...,alpha_k)-multiamicable k-tuples.

The asymptotic density of (alpha_1, alpha_2)-multiamicable pairs relative to the positive integers is 0.

Links

Table of n, a(n) for n=1..31.

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

Formula

We say that the natural numbers n_1,..., n_k form an (alpha_1,...,alpha_k)-multiamicable k-tuple if sigma(n_1)=sigma(n_2)=...=sigma(n_k)=alpha_1n_1+alpha_2n_2+...+alpha_kn_k, where alpha_1,...,alpha_k are positive integers, where sigma(n) is the sum of the divisors of n.

Example

For k=2, alpha_1=1, alpha_2=2 we have (1560, 1740), (7380, 7776), (20664, 22428), (543456, 590112), (588744, 639288),

Prog

(PARI) isok(k) = my(s=sigma(k), m=s-2*k); m>0 && m<k && sigma(m)==s \\ Michel Marcus, Apr 28 2025

Crossrefs

Subsequence of A259302.

Cf. A000203, A005820, A063990, A259180, A125490, A036474, A259303, A292365.

Sequence in context: A043653 A194775 A259302 * A251802 A251324 A184666

Adjacent sequences: A383236 A383237 A383238 * A383240 A383241 A383242

Keyword

nonn

Author

S. I. Dimitrov, Apr 20 2025

Extensions

More terms from Sean A. Irvine, May 04 2025

Status

approved