27405 is a member of OEIS A000332: binomial coefficient binomial(n,4) = n * (n-1) * (n-2) * (n-3)/24. The sequence runs:

0, 0, 0, 0, 1, 5, 15, 35, 70, 126, 210, 330, 495, 715, 1001, 1365, 1820, 2380, 3060, 3876, 4845, 5985, 7315, 8855, 10626, 12650, 14950, 17550, 20475, 23751, 27405, 31465, 35960, 40920,

27405 is a member of OEIS A127666: odd infinitary abundant numbers. The sequence runs:

945, 10395, 12285, 15015, 16065, 17955, 19305, 19635, 21735, 21945, 23205, 23625, 25245, 25935, 26565, 27405, 28215, 28875, 29295, 29835, 31395, 33345, 33495, 33915, 34125, 34155, 34965, 35805, 37125, 38745, 39585, 40635, ...

I touched on this topic in a blog post Unitary Divisors.

27405 is a happy, congruent and amenable number.

27405 can be made into a digit equation as follows:

2 + 7 = 4 + 0 + 5

27405 stabilises after about 75 generations, under Conway's Game of Life rules, to four still life blocks.

27405 is the 105-th heptagonal number.

27405 is an abundant, pseudoperfect and Zumkeller number.