|
Search: id:A068781
|
|
|
| A068781 |
|
Lesser of two consecutive numbers each divisible by a square. |
|
+0
12
|
|
| 8, 24, 27, 44, 48, 49, 63, 75, 80, 98, 99, 116, 120, 124, 125, 135, 147, 152, 168, 171, 175, 188, 207, 224, 242, 243, 244, 260, 275, 279, 288, 296, 315, 324, 332, 342, 343, 350, 351, 360, 363, 368, 375, 387, 404, 423, 424, 440, 459, 475, 476, 495, 507, 512
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Also numbers m such that mu(m)=mu(m+1)=0, where mu is the Moebius-function (A008683); A081221(a(n))>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 10 2003
The sequence contains an infinite family of arithmetic progressions like {36a+8}={8,44,80,116,152,188,...} ={4(9a+2)}. {36a+9} provides 2nd non-square-free terms. Such AP's can be constructed to any term by solution of a system of linear Diophantine equation. - Labos E. (labos(AT)ana.sote.hu), Nov 25 2002
1. 4k^2 + 4k is a member for all k; i.e. 8 times a triangular number is a member. 2. (4k+1) times an odd square - 1 is a member. 3. (4k+3) times odd square is a member. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 24 2003
|
|
EXAMPLE
|
44 is in the sequence because 44 = 2^2 * 11 and 45 = 3^2 * 5.
|
|
MATHEMATICA
|
Select[ Range[2, 600], Max[ Transpose[ FactorInteger[ # ]] [[2]]] > 1 && Max[ Transpose[ FactorInteger[ # + 1]] [[2]]] > 1 &]
|
|
CROSSREFS
|
Cf. A068780, A068140, A068781, A068782, A068783, A068784, A068785.
Cf. A049535, A077647, A078143, A045882.
Sequence in context: A029607 A060476 A048109 this_sequence A038524 A162829 A000118
Adjacent sequences: A068778 A068779 A068780 this_sequence A068782 A068783 A068784
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 04 2002
|
|
|
Search completed in 0.002 seconds
|
