A268681 - OEIS

%I #16 Feb 13 2016 23:19:57

%S 1,1,3,6,12,27,42,105,175,175,385,1408,1474,2566,8677,15607,15607,

%T 39934,39934,133300,264305,559565,1288392,5482695,5493321,5546451,

%U 11088442,11088442,24211552,88854292,88854757,133243378,133243378,133243411,2337205436

%N Sum of unique squarefree numbers in first n rows of Pascal's triangle.

%H Peter Kagey, <a href="/A268681/b268681.txt">Table of n, a(n) for n = 1..250</a>

%H Project Euler, <a href="https://projecteuler.net/problem=203">Problem 203: Squarefree Binomial Coefficients</a>

%e a(5) = 1 + 2 + 3 + 6 = 12 because the squarefree numbers in the first 5 rows of Pascal's triangle are 1, 2, 3, and 6:

%e       1

%e      1 1

%e     1 2 1

%e    1 3 3 1

%e   1 4 6 4 1

%t lim = 35; t = Select[#, SquareFreeQ] & /@ Table[Binomial[n, k], {n, 0, lim}, {k, 0, n}]; Table[Total@ Union[Flatten@ Take[t, n]], {n, lim}] (* _Michael De Vlieger_, Feb 11 2016 *)

%o (PARI) row(n) = vector(n, k, k--; binomial(n-1, k));

%o sqfrow(n) = select(x->issquarefree(x), row(n));

%o lista(nn) = {my(s = 0, vsqf = []); for (n=1, nn, vsqf = concat(vsqf, sqfrow(n)); vsqf = vecsort(vsqf,,8); print1(vecsum(vsqf), ", "););} \\ _Michel Marcus_, Feb 11 2016

%Y Cf. A005117, A007318.

%K nonn

%O 1,3

%A _Peter Kagey_, Feb 10 2016