1105 is the smallest positive integer that is a sum of two positive squares in exactly four different ways, It is also the smallest member of a cluster of three
semiprimes (1105, 1106, 1107) with eight
divisors, and the second-smallest
Carmichael number, after
561, one of the first four Carmichael numbers identified by
R. D. Carmichael in his 1910 paper introducing this concept. Its
binary representation 10001010001 and its
base-4 representation 101101 are both
palindromes, and (because the binary representation has nonzeros only in even positions and its base-4 representation uses only the digits 0 and 1) it is a member of the
Moser–de Bruijn sequence of sums of distinct powers of four. As a number of the form \tfrac{n(n^2+1)}{2} for {{nowrap|n={}13,}} 1105 is the
magic constant for
magic squares, and as a difference of two consecutive fourth powers it is a rhombic dodecahedral number (a type of
figurate number), and a
magic number for
body-centered cubic crystals. These properties are closely related: the difference of two consecutive fourth powers is always a magic constant for an odd magic square whose size is the sum of the two consecutive numbers (here . ==References==