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

1,1

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.

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

Crossrefs

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

Sequence in context: A359238 A320011 A068049 * A171092 A141256 A122921

Adjacent sequences: A297847 A297848 A297849 * A297851 A297852 A297853

Keyword

nonn

Author

Felix Fröhlich, Jan 10 2018

Extensions

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

Status

approved