## John Edensor Littlewood was born on this day 132 years ago.

### Properties of the number 1906:

1906 = 2 × 953 is semiprime and squarefree.1906 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 952 totatives.

1906 has sum of divisors equal to 2862 which is an oblong number.

Reversing the decimal digits of 1906 results in a prime.

1906 is the sum of 2 positive triangular numbers.

1906 is the difference of 2 positive pentagonal numbers in 2 ways.

1906 = 15

^{2}+ 41

^{2}is the sum of 2 positive squares in 1 way.

1906 = 13

^{2}+ 21

^{2}+ 36

^{2}is the sum of 3 positive squares.

1906

^{2}= 1230

^{2}+ 1456

^{2}is the sum of 2 positive squares in 1 way.

1906

^{2}is the sum of 3 positive squares.

1906 is a proper divisor of 431

^{7}- 1.

1906 = '190' + '6' is the concatenation of 2 triangular numbers.

1906 is an emirpimes in (at least) the following bases: 3, 5, 7, 11, 13, 18, 21, 23, 25, 29, 31, 32, 33, 35, 38, 46, 47, 48, 49, 51, 54, 56, 59, 67, 70, 71, 72, 74, 76, 81, 83, 84, 86, 89, 90, 91, 96, and 98.

1906 is palindromic in (at least) the following bases: 28, -19, and -34.

1906 in base 3 = 2121121 and consists of only the digits '1' and '2'.

1906 in base 16 = 772 and consists of only the digits '2' and '7'.

1906 in base 19 = 556 and consists of only the digits '5' and '6'.

1906 in base 27 = 2gg and consists of only the digits '2' and 'g'.

1906 in base 28 = 2c2 and consists of only the digits '2' and 'c'.

1906 in base 43 = 11E and consists of only the digits '1' and 'E'.

### The number 1906 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A006315: Numbers n such that n^32 + 1 is prime.

A077065: Semiprimes of form prime - 1.

A090495: Numbers n such that numerator(Bernoulli(2*n)/(2*n)) is different from numerator(Bernoulli(2*n)/(2*n*(2*n-1))).

A098185: If f(x) = (sum of unitary proper divisors of x) = A063919(x) is iterated, the iteration may lead to a fixed point which is either equals 0 or it is from A002827, a unitary perfect number > 1: 6,60,90,87360... Here initial values are collected for which the iteration ends in a unitary perfect number > 1.

A120186: a(n)=ceiling( sum_{i=1..n-1} a(i)/7), a(1)=1.

A206128: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having nonzero determinant and having the same number of clockwise edge increases as its horizontal and vertical neighbors

A217135: Numbers n such that 3^n - 8 is prime.

A229717: T(n,k)=Number of arrays of length n that are sums of k consecutive elements of length n+k-1 permutations of 0..n+k-2, and no two consecutive rises or falls in the latter permutation

A238340: Number of partitions of 4n into 4 parts.

A281205: T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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