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An economical number has been defined as a frugal number, but also as a number that is either frugal or equidigital. gcd( m , n ) ( greatest common divisor of m and n ) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n ).
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
A highly composite number is a positive integer that has more divisors than all smaller positive integers. ... 8 64 21 10080 5,2,1,1 9 ... 8, 10, 12, 15, 20, 24, 30 ...
The first 15 superior highly composite numbers, 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, 1441440, 4324320, 21621600, 367567200, 6983776800 (sequence A002201 in the OEIS) are also the first 15 colossally abundant numbers, which meet a similar condition based on the sum-of-divisors function rather than the number of divisors. Neither ...
The protons each have an energy of 6.5 TeV, giving a total collision energy of 13 TeV. At this energy, the protons have a Lorentz factor of about 6,930 and move at about 0.999 999 990 c, or about 3.1 m/s (11 km/h) slower than the speed of light (c). It takes less than 90 microseconds (μs) for a proton to travel 26.7 km around the main ring.
An example is calcium-40, with 20 neutrons and 20 protons, which is the heaviest stable isotope made of the same number of protons and neutrons. Both calcium-48 and nickel-48 are doubly magic because calcium-48 has 20 protons and 28 neutrons while nickel-48 has 28 protons and 20 neutrons. Calcium-48 is very neutron-rich for such a relatively ...
126 = 2 + 6 + 12 + 8 + 22 + 32 + 44; 184 = 2 + 6 + 12 + 8 + 22 + 32 + 44 + 58; and so on. This gives all the observed magic numbers and also predicts a new one (the so-called island of stability) at the value of 184 (for protons, the magic number 126 has not been observed yet, and more complicated theoretical considerations predict the magic ...
Even-mass-number nuclides, which comprise 150/251 = ~60% of all stable nuclides, are bosons, i.e., they have integer spin. 145 of the 150 are even-proton, even-neutron (EE) nuclides, which necessarily have spin 0 because of pairing. The remainder of the stable bosonic nuclides are five odd-proton, odd-neutron stable nuclides (2 1 H, 6 3 Li, 10 ...