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 A061304 Squarefree triangular numbers. 10
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 5 00:23 EST 2023. Contains 367565 sequences. (Running on oeis4.)