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number > mathematical constant > Niven's constant

number > number theory > Niven's constant

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Niven's constant

Definición

In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average". More precisely, if we define H(1) = 1 and H(n) = the largest exponent appearing in the unique prime factorization of a natural number n > 1, then Niven's constant is given by

${\\displaystyle \\lim _{n\ o \\infty }{\ rac {1}{n}}\\sum _{j=1}^{n}H(j)=1+\\sum _{k=2}^{\\infty }\\left(1-{\ rac {1}{\\zeta (k)}}\ ight)=1.705211\\dots }$

where ζ is the Riemann zeta function.

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Niven%27s_constant)

Concepto genérico

En otras lenguas

constante de Niven

francés

URI

http://data.loterre.fr/ark:/67375/PSR-TZSTCDZ4-K

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