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A354070 Lesser of an amicable pair in which both members are divisible only by primes congruent to 3 (mod 4). 2
294706414233, 518129600373, 749347913853, 920163589191, 1692477265941, 2808347861781, 3959417614383, 4400950312143, 9190625896683, 10694894578137, 12615883061859, 15028451404659, 18971047742031, 21981625463259, 29768959571967, 37423211019579, 54939420064683, 69202873206621 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

There are 4197267 lesser members of amicable pairs below 10^20 and only 1565 are in this sequence.

The least pair, (294706414233, 305961592167), was discovered by Herman J. J. te Riele in 1995.

The larger counterparts are in A354071.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1565

Ranthony Ashley Clark, Gaussian Amicable Pairs, Thesis, Eastern Kentucky University, 2013.

Patrick Costello and Ranthony Clark, Gaussian Amicable Pairs: "Friendly Imaginary Numbers", 2013.

Patrick Costello and Ranthony A. C. Edmonds, Gaussian Amicable Pairs, Missouri Journal of Mathematical Sciences, Vol. 30, No. 2 (2018), pp. 107-116.

Wikipedia, Gaussian integer.

EXAMPLE

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).

CROSSREFS

Subsequence of A002025 and A004614.

Cf. A001065, A063990, A262623, A262625, A354071.

Sequence in context: A017399 A017663 A345864 * A273936 A287247 A172578

Adjacent sequences:  A354067 A354068 A354069 * A354071 A354072 A354073

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 16 2022

STATUS

approved

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Last modified August 12 11:20 EDT 2022. Contains 356069 sequences. (Running on oeis4.)