cp's OEIS Frontend

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

%I A383239 #47 Jun 01 2025 17:16:19
%S A383239 1740,7776,22428,55968,106140,143910,198792,246510,309582,326196,
%T A383239 411138,421596,428256,590112,639288,697158,870552,941094,958716,
%U A383239 1060956,1087776,1105884,1269828,1341660,1361568,1447620,1495494,1512810,1626324,1727940,1819392
%N A383239 Integers k such that there exists an integer 0<m<k such that sigma(k) = sigma(m) = m + 2*k.
%C A383239 S. I. Dimitrov introduced the notion of (alpha_1,...,alpha_k)-multiamicable k-tuples.
%C A383239 The asymptotic density of (alpha_1, alpha_2)-multiamicable pairs relative to the positive integers is 0.
%H A383239 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024.
%F A383239 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.
%e A383239 For k=2, alpha_1=1, alpha_2=2 we have (1560, 1740), (7380, 7776), (20664, 22428), (543456, 590112), (588744, 639288),
%o A383239 (PARI) isok(k) = my(s=sigma(k)); for (m=1, k-1, if ((sigma(m)==s) && (s==m+2*k), return(m))); \\ _Michel Marcus_, Apr 28 2025
%Y A383239 Cf. A000203, A005820, A063990, A259180, A125490, A036474, A259303, A292365.
%K A383239 nonn
%O A383239 1,1
%A A383239 _S. I. Dimitrov_, Apr 20 2025
%E A383239 More terms from _Sean A. Irvine_, May 04 2025