A195085 Positive integers n for which there exist exactly two integers k in {1,2,3,...,n-1} such that k*n is square.

9, 18, 27, 45, 54, 63, 90, 99, 117, 126, 135, 153, 171, 189, 198, 207, 234, 261, 270, 279, 297, 306, 315, 333, 342, 351, 369, 378, 387, 414, 423, 459, 477, 495, 513, 522, 531, 549, 558, 585, 594, 603, 621, 630, 639, 657, 666, 693, 702, 711, 738, 747, 765, 774, 783

Offset

1,1

Comments

It appears that the terms of this sequence are exactly 9 times those of A005117 and (9/4) times those of A133466.

Also, this sequence gives the positions of those terms where A057918(n)=2.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

Given n=9, {1*9, 2*9, ..., 8*9} = {9,18,27,36,45,54,63,72}, of which 9 and 36 are square. Thus 9 is a term of the sequence.

Prog

(Haskell)
a195085 n = a195085_list !! (n-1)
a195085_list = map (+ 1) $ elemIndices 2 a057918_list
-- Reinhard Zumkeller, Mar 27 2012
(Magma) [k:k in [1..800]|#[m:m in [1..k-1]| IsSquare(m*k)] eq 2]; // Marius A. Burtea, Dec 03 2019

Crossrefs

Cf. A005117, A057918, A133466.

Sequence in context: A083497 A067552 A224977 * A329640 A052489 A034033

Adjacent sequences: A195082 A195083 A195084 * A195086 A195087 A195088

Keyword

nonn

Author

John W. Layman, Sep 08 2011

Status

approved