A064462 -id:A064462 - cp's OEIS frontend

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

Robert G. Wilson v, Oct 02 2001

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

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

Cf. A048277, A064461, A064462.

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} ]

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

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

A064461 First row of Pascal's triangle that has n distinct nonsquarefree entries, or -1 if no such row exists.

Original entry on oeis.org

0, 4, 13, 8, 9, 12, 17, 20, 16, 18, 26, 24, 62, 27, 34, 33, 32, -1, 36, 40, -1, 95, -1, 79, 48, 50, 54, 60, 56, 74, 67, 65, 64, 73, -1, 94, 72, 91, 85, 83, 80, 84, 119, 88, -1, 97, 104, 101, 96, 98, 100, -1, 115, -1, 108, 114, 112, 123, 122, 120, 121, 125, 131

Offset: 0

Robert G. Wilson v, Oct 02 2001

sign

Numbers such that a(n) is -1: 17, 20, 22, 34, 44, 51, ... - Michel Marcus, Mar 05 2014

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

Cf. A064460, A064462, A048276.

f[ n_ ] := (c = 0; k = 1; While[ k < n/2 + .5, If[ Union[ Transpose[ FactorInteger[ Binomial[ n, k ] ] ] [ [ 2 ] ] ] [ [ -1 ] ] > 1, c++ ]; k++ ]; c); Do[ m = 2; While[ f[ m ] != n, m++ ]; Print[ m ], {n, 0, 16} ]

a(n, v) = {for (i=1, #v, if (v[i] == n, return (i-1));); return (-1);} \\ where v is vector A064460; Michel Marcus, Mar 05 2014

Corrected and extended by Michel Marcus, Mar 05 2014

cp's OEIS Frontend

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

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