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A061304
Squarefree triangular numbers.
12
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
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
Sequence in context: A152899 A352212 A342212 * A109442 A360954 A025723
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Apr 26 2001
STATUS
approved