In mathematics, a Størmer number or arc-cotangent irreducible number, named after Carl Størmer, is a positive integer n for which the greatest prime factor of (n2 + 1) meets or exceeds 2n.
The first few Størmer numbers are:
1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, ... (sequence A005528 in the OEIS).J. Todd proved that this sequence is neither finite nor cofinite.
The Størmer numbers arise in connection with the problem of representing the Gregory numbers (arctangents of rational numbers)