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A055086
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n appears 1+[n/2] times.
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10
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0, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The PARI functions t1, t2 can be used to read a triangular array T(n,k) (n >= 0, 0 <= k <= floor(n/2)) by rows from left to right: n -> T(t1(n), t2(n)).
a(n) gives the number of distinct positive values taken by [n/k]. E.g. a(5)=3: [5/{1,2,3,4,5}]={5,2,1,1,1}. - Marc LeBrun (mlb(AT)well.com), May 17 2001
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LINKS
| M. Somos, Sequences used for indexing triangular or square arrays
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FORMULA
| [sqrt(4n+1)]-1.
a(n) = Sum{ A063524(A075993(n, k)): 1<=k<=n} for n>0. - Reinhard Zumkeller, Apr 06 2006
a(n) = ceil(2*sqrt(n+1)) - 2. [Mircea Merca, Feb 05 2012]
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PROG
| (PARI) a(n)=floor(sqrt(4*n+1))-1
(PARI) t1(n)=floor(sqrt(1+4*n)-1) /* A055086 */
(PARI) t2(n)=(1+4*n-sqr(floor(sqrt(1+4*n))))\4 /* A055087 */
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CROSSREFS
| A000267(n)=1+a(n).
Cf. A055087.
Sequence in context: A090501 A126848 A067085 * A001462 A082462 A005041
Adjacent sequences: A055083 A055084 A055085 * A055087 A055088 A055089
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Michael Somos
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