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 A116541 Triangular numbers for which the number of divisors is also a triangular number. 3
 1, 28, 45, 153, 171, 325, 496, 2016, 3321, 4753, 4950, 7260, 7381, 8256, 11628, 13203, 14196, 20100, 29161, 41616, 56953, 64620, 65341, 73536, 76636, 77028, 89676, 90100, 97461, 101475, 126756, 130816, 150975, 166176, 166753, 179700, 180300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Gheorghe Coserea, Table of n, a(n) for n = 1..20000 EXAMPLE 496 is in the sequence because it is a triangular number (31*32/2) and has 10=4*5/2 divisors (1,2,4,8,16,31,62,124,248,496). MAPLE with(numtheory): a:=proc(n) local s: s:=tau(n*(n+1)/2): if type(sqrt(1+8*s)/2-1/2, integer)=true then n*(n+1)/2 else fi end: seq(a(n), n=1..750); # Emeric Deutsch, Apr 06 2006 MATHEMATICA Select[Range[600]*Range[2, 601]/2, IntegerQ@ Sqrt[8 DivisorSigma[0, #] + 1] &] (* Robert G. Wilson v, Apr 20 2006 *) PROG (PARI) seq(N) = {   my(a = vector(N), n = 1, cnt=0);   while (cnt < N,         my(tn = n*(n+1)/2, d = numdiv(tn), x = (sqrtint(1+8*d)-1)\2);         if (x*(x+1)/2 == d, a[cnt++] = tn); n++);   return(a); }; seq(37)  \\ Gheorghe Coserea, Jun 12 2016 CROSSREFS Cf. A000005, A000217. Sequence in context: A180045 A144581 A075875 * A292989 A116565 A305060 Adjacent sequences:  A116538 A116539 A116540 * A116542 A116543 A116544 KEYWORD nonn AUTHOR Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006 EXTENSIONS More terms from Emeric Deutsch, Apr 06 2006 Typos in Mma program corrected by Giovanni Resta, Jun 12 2016 STATUS approved

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Last modified December 13 12:49 EST 2018. Contains 318086 sequences. (Running on oeis4.)