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Search: id:A068781
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| A068781 |
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Lesser of two consecutive numbers each divisible by a square. |
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+0
12
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| 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)
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OFFSET
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1,1
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COMMENT
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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
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EXAMPLE
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44 is in the sequence because 44 = 2^2 * 11 and 45 = 3^2 * 5.
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MATHEMATICA
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Select[ Range[2, 600], Max[ Transpose[ FactorInteger[ # ]] [[2]]] > 1 && Max[ Transpose[ FactorInteger[ # + 1]] [[2]]] > 1 &]
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CROSSREFS
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Cf. A068780, A068140, A068781, A068782, A068783, A068784, A068785.
Cf. A049535, A077647, A078143, A045882.
Adjacent sequences: A068778 A068779 A068780 this_sequence A068782 A068783 A068784
Sequence in context: A029607 A060476 A048109 this_sequence A038524 A162829 A000118
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 04 2002
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