A080392 Numbers k such that A000984(k) mod k = 0 and A080383(k) != 7.

2, 420, 920, 1122, 1218, 1892, 1978, 2444, 2914, 3198, 3782, 4028, 4136, 4292, 4664, 4958, 4960, 5330, 5762, 5986, 6020, 6032, 6710, 6834, 6864, 6882, 6954, 6956, 6968, 7106, 7130, 7140, 7238, 7254, 7448, 7616, 8178, 8190, 8400, 8692, 9462, 9506, 10712, 11060, 11288

Offset

1,1

Comments

Numbers arising in A067348 and not present in A080385.

Even numbers n such that n divides binomial(n, [n/2]) and A010551(n) does not divide j!*(n-j)! exactly 7 times for j = 0..n. - Peter Luschny, Aug 04 2017

Links

David A. Corneth, Table of n, a(n) for n = 1..274 (Terms <= 60000)

Example

A080383(2) = 3;
A080383(420) = 11;
A080383(920) = 11;
A080383(1122) = 9;
A080383(1218) = 9.

Maple

isa := proc(n)  local bn, bm;
if n mod 2 = 0 then bn := binomial(n, iquo(n, 2)):
if modp(bn, n) = 0 then
   bm := (n, j) -> `if`(modp(bn, binomial(n, j)) = 0, 1, 0):
   return 1 <> add(bm(n, j), j=2..iquo(n, 2)-1)
fi fi; false end:
select(isa, [$1..5000]); # Peter Luschny, Aug 04 2017

Mathematica

Do[s=Count[Table[IntegerQ[Binomial[n, Floor[n/2]]/ Binomial[n, j]], {j, 0, n}], True]; s1=IntegerQ[Binomial[n, n/2]/n]; If[ !Equal[s, 7] && Equal[s1, True], Print[n]], {n, 1, 10000}]
(* Second program: *)
Select[Range@ 5000, Function[n, And[Divisible[Binomial[n, n/2], n], Count[Table[Divisible[Binomial[n, Floor[n/2]], Binomial[n, j]], {j, 0, n}], True] != 7]]] (* Michael De Vlieger, Jul 30 2017 *)

Crossrefs

Cf. A000984, A001405, A067348, A080383, A080385.

Sequence in context: A259562 A177321 A365520 * A154541 A119120 A373552

Adjacent sequences: A080389 A080390 A080391 * A080393 A080394 A080395

Keyword

nonn

Author

Labos Elemer, Mar 17 2003

Extensions

More terms from Michael De Vlieger, Jul 30 2017

Status

approved