A064460 Number of distinct nonsquarefree entries in n-th row of Pascal's triangle.

0, 0, 0, 0, 1, 0, 1, 0, 3, 4, 3, 0, 5, 2, 2, 1, 8, 6, 9, 6, 7, 6, 6, 0, 11, 11, 10, 13, 13, 9, 13, 10, 16, 15, 14, 14, 18, 15, 13, 14, 19, 15, 15, 9, 15, 19, 14, 3, 24, 24, 25, 24, 24, 18, 26, 25, 28, 26, 25, 19, 27, 18, 12, 28, 32, 31, 31, 30, 31, 27, 30, 27, 36

Offset: 0

Author

Robert G. Wilson v, Oct 02 2001

Keywords

• easy
• nonn

Examples

			a(13) = 2 because C(13,5) = 3^2*11*13 and C(13,6) = 2^2*3*11*13.
		

Links

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

Crossrefs

Cf. A048277, A064461, A064462.

Programs

Mathematica

f[ n_ ] := (c = 0; k = 1; While[ k < n/2 + .5, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Table[ f[ n ], {n, 0, 100} ]

PARI

a(n) = sum(k=0, n\2, !issquarefree(binomial(n, k))); \\ Michel Marcus, Mar 05 2014

Formula

a(n) + A238337(n) = A008619(n). - R. J. Mathar, Jan 18 2018