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Cototient


The cototient of a positive number n is defined as n-phi(n), where n is the totient function. It is therefore the number of positive integers <=n that have at least one prime factor in common with n.

The first few cototients for n=1, 2, ... are 0, 1, 1, 2, 1, 4, 1, 4, 3, 6, 1, 8, 1, 8, 7, ... (OEIS A051953).


See also

Highly Cototient Number, Totient Function

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References

Browkin, J. and Schinzel, A. "On Integers Not of the Form n-phi(n)." Colloq. Math. 68, 55-58, 1995.Erdős, P. "Über die Zahlen der Form sigma(n)--n und n--phi(n)." Elem. Math. 11, 83-86, 1973.Flammenkamp, A. and Luca, F. "Infinite Families of Noncototients." Colloq. Math. 86, 37-41, 2000.Jamison, R. E. "The Helly Bound for Singular Sums." Disc. Math. 249, 117-133, 2002.Sloane, N. J. A. Sequence A051953 in "The On-Line Encyclopedia of Integer Sequences."Pomerance, C. and Yang, H.-S. "Variant of a Theorem of Erdős on the Sum-Of-Proper-Divisors Function." Math. Comput. 83, 1903-1913, 2014.

Cite this as:

Weisstein, Eric W. "Cototient." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cototient.html

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