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Multiplicative Number Theoretic Function

المؤلف:  Wilf, H.

المصدر:  Generatingfunctionology, 2nd ed. New York: Academic Press

الجزء والصفحة:  p. 58

18-8-2020

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Multiplicative Number Theoretic Function

A multiplicative number theoretic function is a number theoretic function  that has the property

(1)

for all pairs of relatively prime positive integers  and .

If

(2)

is the prime factorization of a number , then

(3)

Multiplicative number theoretic functions satisfy the amazing identity

			(4)
			(5)

where the product is over the primes.

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REFERENCES:

Wilf, H. Generatingfunctionology, 2nd ed. New York: Academic Press, p. 58, 1994.