A279083 Numbers k such that there exists at least one tetrahedral number with exactly k divisors.

1, 3, 4, 6, 8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40

Offset

1,2

Comments

The only odd terms are 1, 3, and 45 (which correspond to the three positive tetrahedral numbers that are square, i.e., 1, 4, and 19600). It is easy to show that no term larger than 6 is semiprime.

A tetrahedral number with exactly 42 divisors would have to be of the form p^6 * q^2 * r, with p, q, and r distinct primes; does such a tetrahedral number exist?

A tetrahedral number with exactly 50 divisors would have to be of the form p^4 * q^4 * r, with p, q, and r distinct primes; does such a tetrahedral number exist?

Additional terms < 200 include (but may not be limited to) 44, 45, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 84, 88, 90, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 192, 196

Links

Table of n, a(n) for n=1..15.

Crossrefs

Cf. A000292, A279081, A279082.

Sequence in context: A192276 A049305 A147606 * A298805 A085147 A367398

Adjacent sequences: A279080 A279081 A279082 * A279084 A279085 A279086

Keyword

nonn,more

Author

Jon E. Schoenfield, Jan 06 2017

Status

approved