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Search: id:A048277
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| A048277 |
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Number of distinct non-square-free numbers among C(n,k), k=0..n. |
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+0
3
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| 0, 0, 0, 0, 2, 0, 1, 0, 6, 8, 5, 0, 9, 4, 3, 2, 15, 12, 17, 12, 13, 12, 11, 0, 21, 22, 19, 26, 25, 18, 25, 20, 31, 30, 27, 28, 35, 30, 25, 28, 37, 30, 29, 18, 29, 38, 27, 6, 47, 48, 49, 48, 47, 36, 51, 50, 55, 52, 49, 38, 53, 36, 23, 56, 63, 62, 61, 60, 61, 54, 59, 54, 71, 66, 57
(list; graph; listen)
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OFFSET
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0,5
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EXAMPLE
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a(13) = 4 because C(13,5) = C(13,8) = 3^2*11*13 and C(13,6) = C(13,7) = 2^2*3*11*13.
If n=20, then C[ 20, k ] is divisible by a square for 13 values of k, i.e. for k = 1, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, so a[ 20 ] = 13.
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MATHEMATICA
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f[ n_ ] := (c = 0; k = 1; While[ k < n, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Table[ f[ n ], {n, 0, 75} ]
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CROSSREFS
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Cf. A005117, A046098, A048276.
Sequence in context: A076694 A095403 A011328 this_sequence A059419 A049218 A022902
Adjacent sequences: A048274 A048275 A048276 this_sequence A048278 A048279 A048280
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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