A116541 - OEIS

%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