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81

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This article is under construction.            

Please do not rely on any information it contains.            


81 is an integer.

Membership in core sequences

Odd numbers ..., 75, 77, 79, 81, 83, 85, 87, ... A005843
Composite numbers ..., 77, 78, 80, 81, 82, 84, 85, ... A002808
Perfect squares ..., 36, 49, 64, 81, 100, 121, 144, ... A000290
Powers of 3 1, 3, 9, 27, 81, 243, 729, 2187, ... A000244
Powers of primes ..., 71, 73, 79, 81, 83, 89, 97, ... A000961
Fourth powers 1, 16, 81, 256, 625, 1296, 2401, ... A000583
Quarter-squares ..., 56, 64, 72, 81, 90, 100, 110, ... A002620
Numbers that are the sum of two squares ..., 73, 74, 80, 81, 82, 85, 89, ... A001481

Sequences pertaining to 81

Numbers such that string 0, 0 occurs in the base 9
representation of but not of .
81, 162, 243, 324, 405, 486, 567, 648, 729, 810, 891, ... A044251
sequence beginning at 81 81, 244, 122, 61, 184, 92, 46, 23, 70, 35, 106, 53, 160, ... A008876

Partitions of 81

PLACEHOLDER

Roots and powers of 81

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

TABLE GOES HERE

Values for number theoretic functions with 81 as an argument

TABLE GOES HERE

Factorization of 81 in some quadratic integer rings

As was mentioned above, 81 is in the square of 3. But it has different factorizations in some quadratic integer rings.

TABLE

REMARKS

Representation of 81 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 80 15 16 17 18 19 20
Representation 1010001 10000 1101 311 213 144 121 100 81 74 69 63 5B 56 51 4D 49 45 41

See also

Some integers
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