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

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Crossrefs

Cf. A020475, A053200.

Programs

Haskell

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

Mathematica

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

Formula

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