cp's OEIS Frontend

A116541 Triangular numbers for which the number of divisors is also a triangular number.

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