A343330 a(n) is the largest odd positive integer that is abundant and has the same prime signature as A279537(n) or 0 if no such integer exists.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 945, 0, 0, 2205, 0, 0, 2835, 0, 0, 15435, 0, 0, 8505, 0, 0, 108045, 0, 0, 11025, 25515, 0, 46305, 0, 0, 756315, 0, 0, 81675, 76545, 0, 324135, 0, 0, 5294205, 0, 0, 540225, 229635, 0, 2268945, 0, 0, 898425, 37059435, 0, 972405, 0, 3781575, 688905, 0, 0, 15882615, 0

Offset: 1

Author

David A. Corneth, Apr 12 2021

Keywords

• nonn

Comments

Odd abundant numbers k have omega(k) >= 3. The zeros in this sequence come from numbers k having omega(k) < 3 in which case no positive integer with that prime signature exists.

Numbers with omega(k) > 3 are excluded by definition as most such numbers have infinitely many cases for that prime signature in which case no largest element exists.

Examples

			a(17) = 945 as A279537(17) = 120 = 2^(3) * 3^(1) * 5^(1) and has prime signature (3, 1, 1). The largest odd positive integer that has prime signature (3, 1, 1) and is abundant is 945.