121

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121 is an integer. It is the only known square of the form $1+p+p^2+p^3+p^4$, where $p$ is prime (in this case, $p=3$).

Membership in core sequences

Odd numbers	..., 114, 116, 118, 121, 122, 124, 126, ...	A005408
Composite numbers	..., 118, 119, 120, 121, 122, 123, 124, ...	A002808
Perfect squares	..., 64, 81, 100, 121, 144, 169, 196, ...	A000290
Central polygonal numbers	..., 79, 92, 106, 121, 137, 154, 172, ...	A000124
Numbers that are the sum of 2 squares	..., 113, 116, 117, 121, 122, 125, 128, ...	A001481
Loeschian numbers	..., 111, 112, 117, 121, 124, 127, 129, ...	A003136

Sequences pertaining to 121

Multiples of 121	121, 242, 363, 484, 605, 726, 847, 968 ...
$3x+1$ sequence starting at 27	..., 161, 484, 242, 121, 364, 182, 91, 274, ...	A008884

Partitions of 121

There are 2056148051 partitions of 121. Of these, there is the of the [FINISH WRITING]

Roots and powers of 121

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

TABLE GOES HERE

Logarithms and 121st powers

In the OEIS specifically and mathematics in general, $\log x$ refers to the natural logarithm of $x$, whereas all other bases are specified with a subscript.

As above, irrational numbers in the following table are truncated to eight decimal places.

TABLE GOES HERE

Values for number theoretic functions with 121 as an argument

TABLE GOES HERE

Factorization of 121 in some quadratic integer rings

As was mentioned above, 121 is the square of 11. But it has different factorizations in some quadratic integer rings.

TABLE GOES HERE

Representation of 121 in various bases

Base	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Representation	1111001	11111	1321	441	321	232	171	144	121	100	A1	94	89	81	79	72	6D	67	61

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