A061304 Squarefree triangular numbers.

1, 3, 6, 10, 15, 21, 55, 66, 78, 91, 105, 190, 210, 231, 253, 406, 435, 465, 561, 595, 703, 741, 861, 903, 946, 1081, 1326, 1378, 1653, 1711, 1770, 1830, 1891, 2145, 2211, 2278, 2346, 2415, 2485, 2701, 2926, 3003, 3081, 3403, 3486, 3570, 3655, 3741, 4186, 4278

Offset: 1

Author

Amarnath Murthy, Apr 26 2001

Keywords

• nonn
• easy

Examples

			105 = 3 * 5 * 7 is a squarefree triangular number.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A215726.

Programs

Maple

# uses code of A000217
isA061304 := proc(n)
    isA000217(n) and issqrfree(n) ;
    simplify(%) ;
end proc:
for n from 1 to 5000 do
    if isA061304(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Oct 05 2017

Mathematica

Select[Accumulate[Range[0, 100]], SquareFreeQ] (* Jean-François Alcover, Apr 17 2020 *)

PARI

isA078779F(f)=for(i=2,#f~, if(f[i,2]>1, return(0))); #f~==0 || f[1,2]==1 || (f[1,2]==2 && f[1,1]==2)
list(lim)=my(v=List(), ok=1); forfactored(n=2, (sqrtint(lim\1*8+1)+1)\2, e=n[2][,2]; if(isA078779F(n[2]), if(ok, listput(v, binomial(n[1],2)), ok=1), ok=0)); Vec(v) \\ Charles R Greathouse IV, Nov 05 2017

Formula

A010054(a(n))*A008966(a(n)) = 1. - Reinhard Zumkeller, Nov 01 2009

a(n) = A000217(A215726(n)). - Zak Seidov, Aug 22 2012