|
|
A114504
|
|
Numbers n such that the n-th hexagonal number is a 6-almost prime.
|
|
0
|
|
|
50, 56, 60, 63, 81, 95, 98, 112, 116, 120, 138, 150, 152, 158, 172, 180, 182, 189, 196, 198, 204, 212, 221, 238, 242, 252, 260, 266, 275, 276, 296, 300, 304, 306, 315, 328, 332, 333, 340, 344, 348, 350, 356, 363, 374, 375, 388, 390, 405, 413, 420, 423, 434, 452, 455, 456, 459, 462, 472
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
There are no prime hexagonal numbers. The n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(1) = 50 because HexagonalNumber(50) = H(50) = 50*(2*50-1) = 4950 = 2 * 3^2 * 5^2 * 11 is a 6-almost prime.
a(2) = 56 because H(56) = 56*(2*56-1) = 6216 = 2^3 * 3 * 7 * 37 is a 6-almost prime.
a(5) = 81 because H(81) = 81*(2*81-1) = 13041 = 3^4 * 7 * 23 is a 6-almost prime.
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
199 replaced by 198 - R. J. Mathar, Dec 22 2010
|
|
STATUS
|
approved
|
|
|
|