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Search: id:A028391
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| A028391 |
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a(n) = n - floor[sqrt(n)]. |
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+0
16
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| 0, 0, 1, 2, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Number of non-squares <= n.
Number of numbers k (<=n) with an even number of divisors - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 07 2002
Construct the pyramid
............a(0)
.......a(1).a(2).a(3)
..a(4).a(5).a(6).a(7).a(8).. etc.
Now circle all the primes and the result will be a pattern very similar to the famous Ulam spiral. - Sam Alexander (amnalexander(AT)yahoo.com), Nov 14 2003
The sequence floor[n-n^(1/2)] gives the same numbers with a different offset. - Mohammad K. Azarian (azarian(AT)evansville.edu), R. J. Mathar and M. F. Hasler, Apr 30 2008
The number of non-zero values of floor (j^2/n) taken over 1 <= j <= n-1.
a(n) = A173517(n) iff n is not a square. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 20 2010]
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REFERENCES
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B. Alspach, K. Heinrich and G. Liu, Orthogonal factorizations of graphs, pp. 13-40 of Contemporary Design Theory, ed. J. H. Dinizt and D. R. SAtinson, Wiley, 1992 (see Theorem 2.7).
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LINKS
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Dick Boland, Introduction to the Square Spine Spiral, 2000-2003 [broken link].
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FORMULA
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a(n) = ceiling( n - sqrt(n) ), as follows from ceiling(-x)=-floor(x). [Corrected by M.F.Hasler, Feb 21 2010]
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CROSSREFS
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Cf. A056847, A000196, A135662 - A135665, A166373.
Adjacent sequences: A028388 A028389 A028390 this_sequence A028392 A028393 A028394
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KEYWORD
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nonn,easy,nice,new
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AUTHOR
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John Mellor (u15630(AT)snet.net)
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of R. J. Mathar, May 01 2008
Comment and cross-reference added by Christopher Hunt Gribble (chris.eveswell(AT)virgin.net), Oct 13 2009
Corrected formula. - M. F. Hasler (MHasler(AT)univ-ag.fr), Feb 21 2010
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