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 A080383 Number of j (0 <= j <= n) such that the central binomial coefficient C(n,floor(n/2)) = A001405(n) is divisible by C(n,j). 10
 1, 2, 3, 4, 3, 6, 3, 6, 3, 6, 3, 6, 7, 10, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 8, 3, 6, 3, 6, 7, 10, 3, 6, 3, 6, 3, 8, 3, 6, 5, 10, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 7, 10, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 7, 10, 3, 6, 3, 6, 7, 10, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..100000 (first 1000 terms from Vincenzo Librandi, terms 1001..9999 from David A. Corneth) EXAMPLE For n <= 500 only a few values of a(n) arise: {1,2,3,4,5,6,7,8,10,11,14}. From Jon E. Schoenfield, Sep 15 2019: (Start) a(n)=1 occurs only at n=0. a(n)=2 occurs only at n=1. a(n)=3 occurs for all even n > 0 such that C(n,j) divides C(n,n/2) only at j = 0, n/2, and n. (This is the case for about 4/9 of the first 100000 terms, and there appear to be nearly as many terms for which a(n)=6.) a(n)=4 occurs only at n=3. For n <= 100000, the only values of a(n) that occur are 1..16, 18, 19, 22, 23, and 26.    k | Indices n (up to 100000) at which a(n)=k   ---+-------------------------------------------------------    1 | 0    2 | 1    3 | 2, 4, 6, 8, 10, 14, 16, 18, 20, 22, 24, ...    4 | 3    5 | 40, 176, 208, 480, 736, 928, 1248, 1440, ... (A327430)    6 | 5, 7, 9, 11, 15, 17, 19, 21, 23, 27, 29, ... (A080384)    7 | 12, 30, 56, 84, 90, 132, 154, 182, 220, ...  (A080385)    8 | 25, 37, 169, 199, 201, 241, 397, 433, ...    (A080386)    9 | 1122, 1218, 5762, 11330, 12322, 15132, ...   (A327431)   10 | 13, 31, 41, 57, 85, 91, 133, 155, 177, ...   (A080387)   11 | 420, 920, 1892, 1978, 2444, 2914, 3198, ...   12 | 1103, 1703, 2863, 7773, 10603, 15133, ...   13 | 12324, 37444   14 | 421, 921, 1123, 1893, 1979, 1981, 2445, ...   15 | 4960, 6956, 13160, 16354, 18542, 24388, ...   16 | 11289, 16483, 36657, 62653, 89183   17 |   18 | 4961, 6957, 12325, 13161, 16355, 18543, ...   19 | 16356, 88510, 92004   20 |   21 |   22 | 16357, 88511, 90305, 92005   23 | 90306   24 |   25 |   26 | 90307 (End) MATHEMATICA Table[Count[Table[IntegerQ[Binomial[n, Floor[n/2]]/Binomial[n, j]], {j, 0, n}], True], {n, 0, 500}] (* adapted by Vincenzo Librandi, Jul 29 2017 *) PROG (PARI) a(n) = my(b=binomial(n, n\2)); sum(i=0, n, (b % binomial(n, i)) == 0); \\ Michel Marcus, Jul 29 2017 (PARI) a(n) = {if(n==0, return(1)); my(bb = binomial(n, n\2), b = n); res = 2 + !(n%2) + 2 * (n>2 && n%2 == 1); for(i = 2, (n-1)\2, res += 2*(bb%b==0); b *= (n + 1 - i) / i); res} \\ David A. Corneth, Jul 29 2017 (MAGMA) [#[j:j in [0..n]| Binomial(n, Floor(n/2)) mod Binomial(n, j) eq 0]:n in [0..100]]; // Marius A. Burtea, Sep 15 2019 CROSSREFS Cf. A001405, A000225, A057977, A022292, A020475, A067348, A042996. Cf. A327430, A080384, A080385, A080386, A327431, A080387. Cf. A080393. Sequence in context: A288778 A290139 A317588 * A086369 A337532 A092089 Adjacent sequences:  A080380 A080381 A080382 * A080384 A080385 A080386 KEYWORD nonn AUTHOR Labos Elemer, Mar 12 2003 EXTENSIONS Edited by Dean Hickerson, Mar 14 2003 Offset corrected by David A. Corneth, Jul 29 2017 STATUS approved

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)