A057918 Number of pairs of numbers (r,s) each less than n such that (r,s,n) is in geometric progression.

0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0, 1, 4, 0, 2, 1, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 3, 6, 4, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 7, 0, 0, 0, 1, 0, 0, 0, 5, 0, 0, 4, 1, 0, 0, 0, 3, 8, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 3, 0, 6, 2, 9, 0, 0, 0, 1, 0

Offset

1,9

Comments

Also, the number of integers k in {1,2,...,n-1} such that k*n is square. - John W. Layman, Sep 08 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000188(n) - 1.

a(A005117(n)) = 0; a(A013929(n)) > 0; A008966(n) = A000007(a(n)); a(A133466(n)) = 1; a(A195085(n)) = 2. - Reinhard Zumkeller, Mar 27 2012

Example

a(72)=5 since (2,12,72), (8,24,72), (18,36,72), (32,48,72), (50,60,72) are the possible three term geometric progressions.

Prog

(Haskell)
a057918 n = sum $ map ((0 ^) . (`mod` n) . (^ 2)) [1..n-1]
-- Reinhard Zumkeller, Mar 27 2012

Crossrefs

Cf. A000188, A005117, A133466.

Cf. A132345 (partial sums).

Sequence in context: A331983 A219485 A337165 * A242192 A016380 A341354

Adjacent sequences: A057915 A057916 A057917 * A057919 A057920 A057921

Keyword

easy,nonn

Author

Henry Bottomley, Nov 22 2000

Status

approved