cp's OEIS Frontend

A354070 Lesser of an amicable pair in which both members are divisible only by primes congruent to 3 (mod 4).

%I A354070 #16 May 17 2022 03:41:18
%S A354070 294706414233,518129600373,749347913853,920163589191,1692477265941,
%T A354070 2808347861781,3959417614383,4400950312143,9190625896683,
%U A354070 10694894578137,12615883061859,15028451404659,18971047742031,21981625463259,29768959571967,37423211019579,54939420064683,69202873206621
%N A354070 Lesser of an amicable pair in which both members are divisible only by primes congruent to 3 (mod 4).
%C A354070 Since the factorization of numbers that are divisible only by primes congruent to 3 (mod 4) is the same also in Gaussian integers, these pairs are also Gaussian amicable pairs.
%C A354070 There are 4197267 lesser members of amicable pairs below 10^20 and only 1565 are in this sequence.
%C A354070 The least pair, (294706414233, 305961592167), was discovered by Herman J. J. te Riele in 1995.
%C A354070 The larger counterparts are in A354071.
%H A354070 Amiram Eldar, <a href="/A354070/b354070.txt">Table of n, a(n) for n = 1..1565</a>
%H A354070 Ranthony Ashley Clark, <a href="https://encompass.eku.edu/etd/158/">Gaussian Amicable Pairs</a>, Thesis, Eastern Kentucky University, 2013.
%H A354070 Patrick Costello and Ranthony Clark, <a href="http://www.ranthonyedmonds.com/uploads/2/5/4/6/25466493/colloquium_presentation.pdf">Gaussian Amicable Pairs: "Friendly Imaginary Numbers"</a>, 2013.
%H A354070 Patrick Costello and Ranthony A. C. Edmonds, <a href="https://doi.org/10.35834/mjms/1544151688">Gaussian Amicable Pairs</a>, Missouri Journal of Mathematical Sciences, Vol. 30, No. 2 (2018), pp. 107-116.
%H A354070 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gaussian_integer">Gaussian integer</a>.
%e A354070 294706414233 is a term since (294706414233, 305961592167) is an amicable pair: A001065(294706414233) = 305961592167 and A001065(305961592167) = 294706414233, 294706414233 = 3^4 * 7^2 * 11 * 19 * 47 * 7559, and 3, 7, 11, 19, 47 and 7559 are all congruent to 3 (mod 4), and 305961592167 = 3^4 * 7 * 11 * 19 * 971 * 2659, and 3, 7, 11, 19, 971 and 2659 are all congruent to 3 (mod 4).
%Y A354070 Subsequence of A002025 and A004614.
%Y A354070 Cf. A001065, A063990, A262623, A262625, A354071.
%K A354070 nonn
%O A354070 1,1
%A A354070 _Amiram Eldar_, May 16 2022