A382628 Centered hexagonal numbers that are sphenic numbers.

3367, 4921, 8911, 9919, 10621, 14911, 18487, 21931, 25669, 27937, 37297, 41419, 55081, 63511, 66157, 72541, 80197, 106597, 108871, 113491, 117019, 130417, 134197, 136747, 139321, 174967, 195841, 198919, 203581, 219511, 226051, 232687, 236041, 244531, 247969, 256669, 258427, 269101, 272707, 287371

Offset: 1

Author

Massimo Kofler, Apr 01 2025

Keywords

• nonn

Comments

All terms are odd.

Examples

			3367 is the 33rd centered hexagonal number and 3367 = 7*13*37 is the product of 3 distinct primes.
8911 is the 54th centered hexagonal number and 8911 = 7*19*67 is the product of 3 distinct primes.
		

Crossrefs

Intersection of A007304 and A003215.

Cf. A113530.

Programs

Mathematica

Select[Table[3*n*(n+1) + 1, {n, 0, 400}], FactorInteger[#][[;; , 2]] == {1, 1, 1} &] (* Amiram Eldar, Apr 01 2025 *)

PARI

select(x->((omega(x)==3) && (bigomega(x)==3)), vector(100, n, 3*n*(n+1) + 1)) \\ Michel Marcus, Apr 02 2025

Formula

a(n) == 1 (mod 6).