A262828 Real positive integers with more than one distinct factorization in Z[sqrt(-5)].

6, 9, 12, 14, 18, 21, 24, 27, 28, 30, 36, 42, 45, 46, 48, 49, 54, 56, 60, 63, 66, 69, 70, 72, 78, 81, 84, 86, 90, 92, 94, 96, 98, 99, 102, 105, 108, 112, 114, 117, 120, 126, 129, 132, 134, 135, 138, 140, 141, 144, 145, 147, 150, 153, 154, 156, 161, 162, 166, 168, 171, 172, 174, 180

Offset: 1

Author

Alonso del Arte, Oct 03 2015

Keywords

• nonn

Comments

To count as distinct from another factorization, a factorization must not be derived from the other by multiplication by units. For example, -2 * -3 is not distinct from 2 * 3 as a factorization of 6.

If a number is in this sequence, then so are all its real positive integer multiples. The negative multiples also have more than one factorization, but of course one has to remember to put in the -1 as needed.

Z[sqrt(-5)] has class number 2. This means that while a number may have more than one factorization, all factorizations have the same number of factors. If one factorization seems to have fewer factors, then it is an incomplete factorization.

Examples

			14 = 2 * 7 = (3 - sqrt(-5))(3 + sqrt(-5)), so 14 is in the sequence.
		

Crossrefs

Cf. A020669 (superset).