561

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Summary

561 is a square-free number with prime factors 3, 11, and 17. The prime factorization is:

$561 = 3 * 11 * 17$

Property or family	Parameter values	First few numbers satisfying the property	Proof of satisfaction/membership/containment
Carmichael number (also called absolute pseudoprime)	first Carmichael number	561, 1105, 1729, 2465, 2821, 6601, [SHOW MORE] 8911, 10585, 15841, 29341, 41041, 46657, 52633, 62745, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 410041, 449065, 488881, 512461 View list on OEIS	The universal exponent is $l c m {3 - 1, 11 - 1, 17 - 1} = 80$ which divides $561 - 1 = 560$
Poulet number (Fermat pseudoprime to base 2)	second Poulet number	341, 561, 645, 1105, 1387, 1729, 1905, 2047, [SHOW MORE] 2465, 2701, 2821, 3277, 4033, 4369, 4371, 4681, 5461, 6601, 7957, 8321, 8481, 8911, 10261, 10585, 11305, 12801, 13741, 13747, 13981, 14491, 15709, 15841, 16705, 18705, 18721, 19951, 23001, 23377, 25761, 29341 View list on OEIS	follows from its being an odd Carmichael number.

Function	Value	Explanation
Euler totient function	320	The Euler totient function is $(3 - 1) (11 - 1) (17 - 1) = (2) (10) (16) = 320$ .
universal exponent	80	The universal exponent is the least common multiple of ${3 - 1, 11 - 1, 17 - 1}$ , which is $l c m {2, 10, 16}$ and equals 80. Note that 561 is a Carmichael number precisely because the universal exponent divides 561 - 1 = 560.
Mobius function	-1	The number is a square-free number and it has an odd number of prime divisors (3 prime divisors).
divisor count function	8	$(1 + 1) (1 + 1) (1 + 1)$ where the first 1s in each sum denote the multiplicities of the prime divisors.
largest prime divisor	17
largest prime power divisor	17