A091813 Number of positive squarefree integers k<=n satisfying gcd_*(k,n)=1, where gcd_*(k,n) is the greatest divisor of k that is also a unitary divisor of n.

1, 1, 2, 3, 3, 2, 5, 6, 6, 3, 7, 6, 8, 5, 6, 11, 11, 8, 12, 10, 8, 9, 15, 12, 16, 10, 17, 14, 17, 8, 19, 20, 13, 13, 15, 23, 23, 15, 17, 21, 26, 11, 28, 26, 24, 18, 30, 23, 31, 20, 21, 29, 32, 22, 25, 29, 23, 23, 36, 23, 37, 25, 34, 39, 30, 18, 41, 39, 29, 22, 44, 45, 45, 30, 35, 44

Offset

1,3

References

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, section 1.7, Unitarism and Infinitarism, pp. 49-56.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Steven R. Finch, Unitarism and Infinitarism, February 25, 2004. [Cached copy, with permission of the author]

Example

a(4)=3 because each of 1, 2, 3 are squarefree and gcd_*(2,4)=1. The latter follows since 2 is not a unitary divisor of 4. a(5)=3 because 4 is not squarefree.

Mathematica

udiv[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; uGCD[a_, b_] := Max[Intersection[Divisors[a], udiv[b]]]; a[n_] := Sum[MoebiusMu[k]^2 * Boole[uGCD[k, n] == 1], {k, 1, n}]; Array[a, 76] (* Amiram Eldar, Oct 01 2019 *)

Crossrefs

Cf. A047994, A073311.

Sequence in context: A095174 A131307 A336168 * A238114 A291300 A345287

Adjacent sequences: A091810 A091811 A091812 * A091814 A091815 A091816

Keyword

nonn

Author

Steven Finch, Mar 07 2004

Status

approved