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%I #16 Jun 12 2016 22:00:40
%S 1,28,45,153,171,325,496,2016,3321,4753,4950,7260,7381,8256,11628,
%T 13203,14196,20100,29161,41616,56953,64620,65341,73536,76636,77028,
%U 89676,90100,97461,101475,126756,130816,150975,166176,166753,179700,180300
%N Triangular numbers for which the number of divisors is also a triangular number.
%H Gheorghe Coserea, <a href="/A116541/b116541.txt">Table of n, a(n) for n = 1..20000</a>
%e 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).
%p 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
%t Select[Range[600]*Range[2, 601]/2, IntegerQ@ Sqrt[8 DivisorSigma[0, #] + 1] &] (* _Robert G. Wilson v_, Apr 20 2006 *)
%o (PARI)
%o seq(N) = {
%o my(a = vector(N), n = 1, cnt=0);
%o while (cnt < N,
%o my(tn = n*(n+1)/2, d = numdiv(tn), x = (sqrtint(1+8*d)-1)\2);
%o if (x*(x+1)/2 == d, a[cnt++] = tn); n++);
%o return(a);
%o };
%o seq(37) \\ _Gheorghe Coserea_, Jun 12 2016
%Y Cf. A000005, A000217.
%K nonn
%O 1,2
%A Luc Stevens (lms022(AT)yahoo.com), Apr 03 2006
%E More terms from _Emeric Deutsch_, Apr 06 2006
%E Typos in Mma program corrected by _Giovanni Resta_, Jun 12 2016
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