OFFSET
1,2
COMMENTS
a(47) = 1728896400 is the product of two distinct triangular numbers in two different ways. 1728896400 = A000217(8) * A000217(9800) = A000217(27) * A000217(3024). - Donovan Johnson, Sep 01 2012
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..1000
Erich Friedman, What's Special About This Number? (See entry 7056.)
FORMULA
a(n) = (A175497(n))^2. [From R. J. Mathar, Jun 03 2010]
EXAMPLE
Examples: 900=3*300. 7056 = 6*1176. 1368900 = 6*228150. 44100 = 36*1225.
PROG
(PARI) istriangular(n)=issquare(8*n+1)
isok(n) = {if (issquare(n), d = divisors(n); fordiv(n, d, if (d > sqrtint(n), break); if ((d != n/d) && istriangular(d) && istriangular(n/d), return (1)); ); ); return (0); } \\ Michel Marcus, Jul 24 2013
(Python)
from itertools import count, islice, takewhile
from sympy import divisors
from sympy.ntheory.primetest import is_square
def A169836_gen(): # generator of terms
return filter(lambda k:not k or any(map(lambda d: is_square((d<<3)+1) and is_square((k//d<<3)+1), takewhile(lambda d:d**2<k, divisors(k)))), (m**2 for m in count(0)))
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, May 30 2010
EXTENSIONS
More terms from R. J. Mathar, Jun 03 2010
STATUS
approved