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 A116990 Indices of triangular numbers whose sum of divisors is square. 4
 1, 2, 11, 20, 40, 68, 92, 212, 236, 253, 266, 321, 328, 452, 582, 589, 596, 668, 695, 716, 782, 788, 836, 928, 932, 970, 991, 1012, 1065, 1076, 1173, 1264, 1300, 1336, 1388, 1436, 1490, 1549, 1796, 1854, 1927, 1995, 2159, 2228, 2252, 2468, 2545, 2588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Zak Seidov, Oct 19 2010: (Start) A074285(n) = A000203(A000217(n)) = s^2. Corresponding values of s begin: 1,2,12,24,42,72,96,216,240,192,240,288,336,456,504, 480,600,672,840,720,720,792,960,930,936,756,992,936,1008,1080,... (are most values of s multiples of 3?). (End) LINKS Zak Seidov, Table of n, a(n) for n = 1..561 FORMULA n such that A074285(n) is in A000290. n such that sum( d | A000217(n), d ) is in A000290. n such that A000203(A000217(n)) is in A000290. n such that sum( d | n*(n+1)/2, d ) = k^2 for integer k. EXAMPLE a(1) = 1 because sigma(1*2/2) = sigma(1) = 1 = 1^2, a(2) = 2 because sigma(2*3/2) = sigma(3) = 2^2, a(3) = 11 because sigma(11*12/2) = sigma(66) = 144 = 12^2. MAPLE with(numtheory): a:=proc(n) if type(sqrt(sigma(n*(n+1)/2)), integer)=true then n else fi end: seq(a(n), n=0..3100); # Emeric Deutsch, Apr 06 2006 MATHEMATICA Flatten@ Position[Accumulate[Range@ 2600], n_ /; IntegerQ@ Sqrt@ DivisorSigma[1, n] == True] (* Michael De Vlieger, Mar 17 2015 *) PROG (PARI) for(n=1, 1000, if(issquare(sigma(n*(n+1)/2)), print1(n", "))) \\ Zak Seidov, Mar 21 2015 CROSSREFS See also: A000217 Triangular numbers: a(n) = C(n+1,2) = n(n+1)/2 = 0+1+2+...+n. A074285 Sum of the divisors of n-th triangular number. A083675 Triangular number for which the sum of the proper divisors is also a triangular number. A000203 sigma(n) = sum of divisors of n. Also called sigma_1(n). Cf. A000203, A000217, A000290, A074285, A083675. Sequence in context: A279774 A092595 A175927 * A279772 A226416 A146087 Adjacent sequences:  A116987 A116988 A116989 * A116991 A116992 A116993 KEYWORD easy,nonn,less AUTHOR Jonathan Vos Post, Apr 04 2006 EXTENSIONS More terms from Emeric Deutsch, Apr 06 2006 Incorrect term 0 removed by Michel Marcus, Mar 17 2015 STATUS approved

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Last modified April 23 21:25 EDT 2019. Contains 322388 sequences. (Running on oeis4.)