A297850 - OEIS

%I #53 Dec 13 2020 09:56:04

%S 2,2,2,2,2,2,3,2,2,2,3,3,2,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,

%T 2,2,2,3,2,2,3,2,2,2,2,3,2,3,2,3,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,3,2,2,2,2,2,3,2,2,2,3,2,2,3,2,2

%N Least common prime factor of the members of n-th amicable pair, or 0 if the two members of the pair are coprime.

%C The question whether a(n) = 0 for any n is an open problem.

%C This is different from A171092 (cf. Chernykh link).

%C If a(n) = 0, then A001221(A259180(2*n-1)*A259180(2*n)) > 21 (cf. Hagis, 1975).

%H Amiram Eldar, <a href="/A297850/b297850.txt">Table of n, a(n) for n = 1..10000</a>

%H Sergei Chernykh, <a href="https://sech.me/ap/news.html#20160130">Amicable pairs news</a>

%H Peter Hagis, Jr., <a href="http://www.jstor.org/stable/2690064">On the Number of Prime Factors of a Pair of Relatively Prime Amicable Numbers</a>, Mathematics Magazine, Vol. 48, No. 5 (1975), pp. 263-266.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Amicable_numbers">Amicable numbers</a>.

%F a(n) = A297934(A259180(2*n), A259180(2*n-1)).

%F a(n) = A020639(A061469(n)), if A061469(n) > 1 and 0 otherwise. - _Amiram Eldar_, Dec 13 2020

%Y Cf. A002025, A020639, A061469, A122967, A171092, A259180, A297934.

%K nonn

%O 1,1

%A _Felix Fröhlich_, Jan 10 2018

%E Offset corrected and more terms added by _Amiram Eldar_, Dec 13 2020