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Like many other powers of 5, it is a Friedman number in base 10 since 125 = 5 1 + 2. 125 is the center of a close triplet of perfect powers , (121 = 11 2 , 125 = 5 3 , 128 = 2 7 ). Excluding the trivial cases of 0 and 1, the only closer such triplet is (4,8,9) and the only other equally close is (25, 27, 32).
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The smallest odd integer with abundancy index exceeding 3 is 1018976683725 = 3 3 × 5 2 × 7 2 × 11 × 13 × 17 × 19 × 23 × 29. [8] If p = (p 1, ..., p n) is a list of primes, then p is termed abundant if some integer composed only of primes in p is abundant. A necessary and sufficient condition for this is that the product of p i /(p i − ...
12 (twelve) is the natural number following 11 and preceding 13.. Twelve is the 3rd superior highly composite number, [1] the 3rd colossally abundant number, [2] the 5th highly composite number, and is divisible by the numbers from 1 to 4, and 6, a large number of divisors comparatively.
11 p − 1 ≡ 1 (mod p 2): 71 [20] 12 p − 1 ≡ 1 (mod p 2): 2693, 123653 (OEIS: ...
For example, 2 × 3 2 × 29 × 823 = 429606 is practical, because the inequality above holds for each of its prime factors: 3 ≤ σ(2) + 1 = 4, 29 ≤ σ(2 × 3 2) + 1 = 40, and 823 ≤ σ(2 × 3 2 × 29) + 1 = 1171. The condition stated above is necessary and sufficient for a number to be practical.
The 125 S was powered by Gioacchino Colombo's 1.5 L (1497 cc/91 in³) 60° V12 with a bore/stroke of 55 x 52.5 mm . This engine produced 118 bhp (87 kW) at 6,800 rpm with a compression ratio of 9.5:1. It was a single overhead camshaft design with 2 valves per cylinder and three double-choke Weber 30DCF carburettors.
Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form (with x being 2 and 5, respectively). [2] It is also a star number, a centered tetrahedral number, and a centered octagonal number.