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A262828
Real positive integers with more than one distinct factorization in Z[sqrt(-5)].
1
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
1,1
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.
EXAMPLE
14 = 2 * 7 = (3 - sqrt(-5))(3 + sqrt(-5)), so 14 is in the sequence.
CROSSREFS
Cf. A020669 (superset).
Sequence in context: A272466 A267918 A330703 * A306647 A189728 A214777
KEYWORD
nonn
AUTHOR
Alonso del Arte, Oct 03 2015
STATUS
approved