A007012 a(n) is number of k for which C(n,k) is not divisible by n. (Formerly M0248)

1, 0, 2, 2, 3, 2, 5, 2, 5, 4, 5, 2, 8, 2, 9, 8, 9, 2, 9, 2, 11, 8, 9, 2, 15, 6, 9, 10, 15, 2, 20, 2, 17, 8, 5, 10, 15, 2, 9, 10, 19, 2, 23, 2, 19, 20, 17, 2, 29, 8, 17, 20, 19, 2, 29, 10, 24, 8, 17, 2, 35, 2, 33, 18, 33, 16, 19, 2, 11, 20, 27, 2, 33, 2, 9, 30, 19, 16, 41, 2, 31, 28, 9, 2, 32, 16

Offset

0,3

Comments

The number of nonzero terms in the polynomial (1+x)^n (mod n). Note that n is prime iff a(n)=2. - T. D. Noe, Feb 23 2006

For n > 0: a(n) = number of terms > 0 in n-th row of triangle A053200. - Reinhard Zumkeller, Jan 24 2014

References

J. H. Conway, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Formula

a(n) = n + 1 - A020475(n). - T. D. Noe, Feb 23 2006

Mathematica

Prepend[ Array[ Length[ Select[ Table[ Binomial[ #, k ]/#, {k, 0, #} ], !IntegerQ[ # ]& ] ]&, 100 ], 1 ]

Prog

(Haskell)
a007012 n = a007012_list !! n
a007012_list = 1 : map (sum . map signum) (tail a053200_tabl)
-- Reinhard Zumkeller, Jan 24 2014

Crossrefs

Cf. A020475, A053200.

Sequence in context: A323347 A322900 A238791 * A343371 A298423 A319810

Adjacent sequences: A007009 A007010 A007011 * A007013 A007014 A007015

Keyword

nonn

Author

N. J. A. Sloane

Status

approved