

A086222


a(n) = card{ (x,y,z)  x <= y <= z and lcm(x,y,z) = n }.


4



1, 3, 3, 6, 3, 13, 3, 10, 6, 13, 3, 30, 3, 13, 13, 15, 3, 30, 3, 30, 13, 13, 3, 54, 6, 13, 10, 30, 3, 71, 3, 21, 13, 13, 13, 73, 3, 13, 13, 54, 3, 71, 3, 30, 30, 13, 3, 85, 6, 30, 13, 30, 3, 54, 13, 54, 13, 13, 3, 178, 3, 13, 30, 28, 13, 71, 3, 30, 13, 71, 3, 135, 3, 13, 30, 30, 13, 71, 3
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OFFSET

1,2


COMMENTS

A number of conjectures are possible, many of which should be easy to prove. Examples: (1) If n is a product of two primes then a(n)=13. (2) If n is a square of a prime then a(n)=6.  John W. Layman, Sep 01 2003


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000


FORMULA

For a prime p, a(p) = 3.
a(n) = (A070919(n) + 3*A048691(n) + 2)/6.  Vladeta Jovovic, Dec 01 2004


PROG

(PARI)
A048691(n) = numdiv(n^2);
A070919(n) = sumdiv(n, d, (numdiv(d)^3)*moebius(n/d));
A086222(n) = ((A070919(n)+3*A048691(n)+2)/6); \\ Antti Karttunen, May 19 2017, after Jovovic's formula.


CROSSREFS

Cf. A048691, A070919, A018892, A086165.
Sequence in context: A323349 A307982 A120909 * A278663 A086492 A143305
Adjacent sequences: A086219 A086220 A086221 * A086223 A086224 A086225


KEYWORD

nonn


AUTHOR

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 28 2003


EXTENSIONS

More terms from John W. Layman, Sep 01 2003


STATUS

approved



