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Search: id:A068310
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| A068310 |
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n^2 - 1 divided by its largest square divisor. |
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+0
5
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| 3, 2, 15, 6, 35, 3, 7, 5, 11, 30, 143, 42, 195, 14, 255, 2, 323, 10, 399, 110, 483, 33, 23, 39, 3, 182, 87, 210, 899, 15, 1023, 17, 1155, 34, 1295, 38, 1443, 95, 1599, 105, 1763, 462, 215, 506, 235, 138, 47, 6, 51, 26, 2703, 78, 2915, 21, 3135, 203, 3363, 870, 3599
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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In other words, squarefree part of n^2-1.
Least m for which x^2 - m*y^2 = 1 has a solution with x = n.
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EXAMPLE
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a(6) = 35, as 6^2 - 1 = 35 itself is squarefree.
7^2-1 = 48, whose largest square divisor is 16, so a(7) = 48/16=3.
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MATHEMATICA
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a[n_] := Times@@(#[[1]] ^ Mod[ #[[2]], 2]&/@FactorInteger[n^2-1])
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PROGRAM
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(PARI) a(n) = core(n*n - 1). - David Wasserman (wasserma(AT)spawar.navy.mil), Mar 07 2005
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CROSSREFS
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a(n) = A007913(n^2-1).
Cf. A002350, A067872, A033314.
Adjacent sequences: A068307 A068308 A068309 this_sequence A068311 A068312 A068313
Sequence in context: A064536 A055234 A086485 this_sequence A033314 A070260 A072346
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 25 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean(AT)math.ucdavis.edu), Mar 19 2002
Entry revised by njas, Apr 27 2007
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