66

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66 is an integer, the number of 8-iamonds.

Membership in core sequences

Even numbers	..., 60, 62, 64, 66, 68, 70, 72, ...	A005843
Composite numbers	..., 63, 64, 65, 66, 68, 69, 70, ...	A002808
Abundant numbers	..., 54, 56, 60, 66, 70, 72, 78, ...	A005101
Triangular numbers	..., 36, 45, 55, 66, 78, 91, 105, ...	A000217
Squarefree numbers	..., 61, 62, 65, 66, 67, 69, 70, ...	A005117

In Pascal's triangle, 66 occurs only twice, namely in row 66, in the second and next to last positions. But it also appears in a subtler way, as the sum of the numbers in row 6: 1 + 6 15 + 20 + 15 + 6 + 1 = 66.

Sequences pertaining to 66

Multiples of 66	0, 66, 132, 198, 264, 330, 396, 462, 528, 594, 660, 726, 792, ...
Divisors of 66	1, 2, 3, 6, 11, 22, 33, 66	A018268
$3x-1$ sequence starting at 66	66, 33, 98, 49, 146, 73, 218, 109, 326, 163, 488, 244, 122, 61, ...	A008896

Partitions of 66

There are 1741630 partitions of 66.

The Goldbach representations of 66 are: 61 + 5 = 59 + 7 = 53 + 13 = 47 + 19 = 43 + 23 = 37 + 29 = 66.

Roots and powers of 66

In the table below, irrational numbers are given truncated to eight decimal places.

TABLE GOES HERE

Values for number theoretic functions with 66 as an argument

TABLE GOES HERE

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −66, 66

The commutative quadratic integer ring with unity [FINISH WRITING]

TABLE GOES HERE

Factorization of 66 in some quadratic integer rings

In $\mathbb {Z}$, 66 has the prime factorization of 2 × 3 × 11. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

Representation of 66 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	1000010	2110	1002	231	150	123	102	73	66	60	56	51	4A	46	42	3F	3C	39	36

See also

Some integers

							$-1$
0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
40	41	42	43	44	45	46	47	48	49
					1729