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

1,2

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000217, A215726.

Sequence in context: A152899 A352212 A342212 * A109442 A360954 A025723

Adjacent sequences: A061301 A061302 A061303 * A061305 A061306 A061307

Keyword

nonn,easy

Author

Amarnath Murthy, Apr 26 2001

Status

approved