1000: cube of 10 1024: tenth power of 2 1184: Paganini’s number 1210: the number amicable to Paganini’s number 1225: square of 35 1331: cube of 11 1444: square of 38 1681: square of 41 1728: cube of 12 1729: Hardy’s taxicab number 1854: subfactorial 7 2025: square of 45 2047: first composite Mersenne number … Continue reading famous 4-digit numbers →

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Definition. (suggested new terminology) If n is an even perfect number, then the statement that p is the generating prime for n means that p is the integer such that n = (2^(p – 1))*(2^p – 1). The following theorem is posted on Mathematics Stack Exchange: Theorem. If n is an even perfect number, then … Continue reading a result on perfect numbers on Mathematics Stack Exchange →

An even number is perfect if, and only if, its cototient is the square of the highest power of 2 contained in it. Details: For even n, call the highest power of 2 that divides n bouba(n), and call n/bouba(n) kiki(n). (Saying that a number is ‘totally kiki’ (or, ‘purely kiki’) is just a picturesque … Continue reading Cototient characterization of even perfect numbers →

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