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
Day: July 18, 2020
Pisano periods
Here is the link to the Wikipedia article on that topic. keywords: [Fibonacci sequence] [Number Theory] [Mathematics] [periodicity]
article: Some conditional results on primes between consecutive squares
Here is the link. keywords: [Mathematics] [Number Theory] [open problems]
a result on perfect numbers on Mathematics Stack Exchange
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
Cototient characterization of even perfect numbers
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
article: The Humble Sum of Remainders Function
Here is the link. keywords: [Mathematics] [Number Theory] [backward difference operator]
‘has a convergent reciprocal sum’
Here is the link to a page containing this expression. keywords: [Mathematics] [Number Theory] [convergence] [sequence] [progression]
harmonic divisor numbers
Here is the link to the Wikipedia article on this topic. keywords: [Mathematics] [Number Theory] [divisibility]
radical of a number
Here is the link to the Wikipedia article on this topic. keywords: [Mathematics] [Number Theory] [square-free number] [square free number] [rad(n)]