77

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77 is an integer, the largest number that can't be written as a sum of distinct numbers whose reciprocals sum to 1.

Membership in core sequences

Odd numbers	..., 71, 73, 75, 77, 79, 81, 83, ...	A005843
Composite numbers	..., 74, 75, 76, 77, 78, 80, 81, ...	A002808
Semiprimes	..., 65, 69, 74, 77, 82, 85, 86, ...	A001358
Squarefree numbers	..., 71, 73, 74, 77, 78, 79, 82, ...	A005117

Sequences pertaining to 77

Multiples of 77	77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, 924, ...
$3x+1$ sequence beginning at 51	51, 154, 77, 232, 116, 58, 29, 88, 44, 22, 11, 34, 17, 52, ...	A008883

Partitions of 77

There are 10619863 partitions of 77. Of these, the of the [FINISH WRITING]

Roots and powers of 77

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

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Logarithms and 77th powers

REMARKS

TABLE

Values for number theoretic functions with 77 as an argument

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Factorization of some small integers in a quadratic integer ring adjoining ${\sqrt {-77}}$, ${\sqrt {77}}$

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$n$	${\mathcal {O}}_{\mathbb {Q} ({\sqrt {77}})}$
2	Prime
3
4	2 2
5	Prime
6	2 × 3
7	$(-1)\left({\frac {7}{2}}-{\frac {\sqrt {77}}{2}}\right)\left({\frac {7}{2}}+{\frac {\sqrt {77}}{2}}\right)$
8	2 3
9	3 2
10	2 × 5
11	$\left({\frac {11}{2}}-{\frac {\sqrt {77}}{2}}\right)\left({\frac {11}{2}}+{\frac {\sqrt {77}}{2}}\right)$
12	2 2 × 3
13	$(-1)\left({\frac {5}{2}}-{\frac {\sqrt {77}}{2}}\right)\left({\frac {5}{2}}+{\frac {\sqrt {77}}{2}}\right)$
14	$(-1)2\left({\frac {7}{2}}\pm {\frac {\sqrt {77}}{2}}\right)$
15	3 × 5
16	2 4
17	$(-1)\left({\frac {3}{2}}-{\frac {\sqrt {77}}{2}}\right)\left({\frac {3}{2}}+{\frac {\sqrt {77}}{2}}\right)$
18	2 × 3 2
19	$(-1)\left({\frac {1}{2}}-{\frac {\sqrt {77}}{2}}\right)\left({\frac {1}{2}}+{\frac {\sqrt {77}}{2}}\right)$
20	2 2 × 5

MORE REMARKS

Factorization of 77 in some quadratic integer rings

PLACEHOLDER

TABLE GOES HERE

Representation of 77 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	1001101	2212	1031	302	205	140	115	85	77	70	65	5C	57	52	4D	49	45	41	3H

REMARKS GO HERE

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