A297850 Least common prime factor of the members of n-th amicable pair, or 0 if the two members of the pair are coprime.

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, 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, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 3, 2, 2

Offset: 1

Author

Felix Fröhlich, Jan 10 2018

Keywords

• nonn

Comments

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

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

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Sergei Chernykh, Amicable pairs news
• Peter Hagis, Jr., On the Number of Prime Factors of a Pair of Relatively Prime Amicable Numbers, Mathematics Magazine, Vol. 48, No. 5 (1975), pp. 263-266.
• Wikipedia, Amicable numbers.

Crossrefs

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

Formula

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

a(n) = A020639(A061469(n)), if A061469(n) > 1 and 0 otherwise. - Amiram Eldar, Dec 13 2020

Extensions

Offset corrected and more terms added by Amiram Eldar, Dec 13 2020