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Sum functions of k-ary and semi-k-ary divisors

Published online by Cambridge University Press:  09 April 2009

D. Suryanarayana  and
V. Siva Rama Prasad
D. Suryanarayana
Affiliation:
Department of Mathematics Andhra University Waltair, India
V. Siva Rama Prasad
Affiliation:
Department of Mathematics A. M. Jain CollegeMeenambakkam Madras-61, India
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It is known that a divisor d>0 of the positive integer n is called unitary [3;§ 1] if dδ = n and (d, δ) = 1, where (d, δ) denotes the g.c.d. of d and δ. We write d¶. Let k be a fixed positive integer. A positve integer n is called k-free if n is not divisible by the kth power of any prime.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 148 - 162
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Chidambaraswamy, J., ‘Sum functions of unitary and semi-unitary divisors,’ The Journal of the Indian Mathematical Society 31 (1967), 117–126.Google Scholar
[2]Cohen, E., ‘Some totient functions’ Duke Mathematical Journal 23 (1956), 515–522.CrossRefGoogle Scholar
[3]Cohen, E., ‘Arithmetical functions associated with the unitary divisiors of an integer,’ Mathematische Zeitzchrift 74 (1960), 66–80.CrossRefGoogle Scholar
[4]Dickson, L. E., History of the theory of numbers, vol. I, (Chelsea publishing company, New York (reprinted) 1952).Google Scholar
[5]Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers, 4th edn. (Oxford (1965).Google Scholar
[6]Klee, V. L., ‘A generalization of Euler's function’, American Mathematical Monthly 55 (1948), 358–359.CrossRefGoogle Scholar
[7]McCarthy, P. J., ‘On a certain family of Arithmetical functions’, American Mathematical Monthly 65 (1958), 586–590.CrossRefGoogle Scholar
[8]Satyanarayana, U. V. and Sastry, K. Pattabhirama, ‘A note on the generalized φ-functions’, Mathematics student 33 (1965), 81–83.Google Scholar
[9]Suryanarayana, D., ‘The number of k-ary divisors of an integer,’ Monatschefte für Mathematik 72 (1968), 445–450.CrossRefGoogle Scholar
[10]Suryanarayana, D., ‘Two arithmetic functions and asymptotic densities of related sets’, Portugaliae Mathematica 31 (1972), 1–11.Google Scholar
[11]Suryanarayana, D., ‘The greatest divisor of n which is prime to k’, Mathematics student 37 (1969), 147–157.Google Scholar
[12]Suryanarayana, D., ‘Some theorems concerning the k-ary divisors of an integer’ Mathematics student 39 (1971), 384–394.Google Scholar