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URL: https://oeis.org/A116541

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A116541
Triangular numbers for which the number of divisors is also a triangular number.
4
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
OFFSET
1,2
LINKS
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
Sequence in context: A144581 A075875 A332764 * A292989 A116565 A305060
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