35 is the sum of the first five
triangular numbers, making it a
tetrahedral number.
[1]
35 is the 10th discrete
semiprime (5×7
)
[2] and the first with
5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.
35 has two
prime factors, (
5 and
7) which also form its main factor pair (5 x 7) and comprise the second
twin-prime distinct
semiprime pair.
The aliquot sum of 35 is
13, within an
aliquot sequence of only one composite number (35,
13,
1,0) to the Prime in the
13-aliquot tree. 35 is the second
composite number with the aliquot sum
13; the first being the cube
27.
35 is the last member of the first triple cluster of semiprimes
33,
34, 35. The second such triple distinct semiprime cluster is
85,
86, and
87.
[3]
35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "
combination of seven things taken three at a time".
35 is a
centered cube number,
[4] a
centered tetrahedral number, a
pentagonal number,
[5] and a
pentatope number.
[6]
35 is a
highly cototient number, since there are more solutions to the equation �−�(�)=35
than there are for any other integers below it except 1.
[7]
There are 35 free
hexominoes, the
polyominoes made from six squares.
Since the greatest prime factor of 352+1=1226
is 613, which is more than 35 twice, 35 is a
Størmer number.
[8]
35 is the highest number one can count to on one's fingers using
senary.
35 is the number of quasigroups of order 4.
35 is the smallest
composite number of the form 6�+5
, where k is a non-negative integer.