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Ω(n), the prime omega function, is the number of prime factors of n counted with multiplicity (so it is the sum of all prime factor multiplicities). A prime number has Ω(n) = 1. The first: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (sequence A000040 in the OEIS). There are many special types of prime numbers. A composite number has Ω(n) > 1.
The sum of its factors (including one and itself) sum to 360, exactly three times 120. Perfect numbers are order two ( 2-perfect ) by the same definition. 120 is the sum of a twin prime pair (59 + 61) and the sum of four consecutive prime numbers (23 + 29 + 31 + 37), four consecutive powers of two (8 + 16 + 32 + 64), and four consecutive powers ...
The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n). For example, 3 is a divisor of 21, since 21/7 = 3 (and therefore 7 is also a divisor of 21). If m is a divisor of n, then so is −m. The tables below only ...
In his 1820 book The Philosophy of Arithmetic, [7] mathematician John Leslie published a multiplication table up to 1000 × 1000, which allows numbers to be multiplied in triplets of digits at a time. Leslie also recommended that young pupils memorize the multiplication table up to 50 × 50.
Two types of factors can be derived from a Cunningham number without having to use a factorization algorithm: algebraic factors of binomial numbers (e.g. difference of two squares and sum of two cubes), which depend on the exponent, and aurifeuillean factors, which depend on both the base and the exponent.
The table is complete up to the maximum norm at the end of the table in the sense that each composite or prime in the first quadrant appears in the second column. Gaussian primes occur only for a subset of norms, detailed in sequence OEIS : A055025 .
In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).
7 210 Yes No 5 30 11 2 310: Yes Yes 6 30 13 30 030: No Yes 7 210 17 510 510: No No 8 210 19 9 699 690: No No 9 210 23 223 092 870: No No 10 210 29 6 469 693 230: No No 11 2 310: 31 200 560 490 130: Yes No 12 2 310: 37 7 420 738 134 810: No No 13 30 030: 41 304 250 263 527 210: No Yes 14 30 030: 43 13 082 761 331 670 030: No No 15 30 030: 47 614 ...
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