## Carl Friedrich Gauss was born on this day 239 years ago.

## Claude Shannon was born on this day 100 years ago.

### Properties of the number 12350:

12350 = 2 × 5^{2}× 13 × 19 is the 10874

^{th}composite number and is not squarefree.

12350 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 4320 totatives.

12350 has a prime digit sum 11 in base 10.

12350 is the difference of 2 positive pentagonal numbers in 3 ways.

12350 = 2

^{2}+ 5

^{2}+ 111

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

12350

^{2}= 7410

^{2}+ 9880

^{2}= 3040

^{2}+ 11970

^{2}= 6270

^{2}+ 10640

^{2}= 4750

^{2}+ 11400

^{2}= 3458

^{2}+ 11856

^{2}= 1368

^{2}+ 12274

^{2}= 7752

^{2}+ 9614

^{2}is the sum of 2 positive squares in 7 ways.

12350

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

12350 is a divisor of 1901

^{3}- 1.

12350 is palindromic in (at least) the following bases: 18, and 31.

12350 in base 18 = 2222 and consists of only the digit '2'.

12350 in base 25 = jj0 and consists of only the digits '0' and 'j'.

12350 in base 31 = cqc and consists of only the digits 'c' and 'q'.

12350 in base 33 = bb8 and consists of only the digits '8' and 'b'.

12350 in base 55 = 44U and consists of only the digits '4' and 'U'.

### The number 12350 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A005587: n(n+5)(n+6)(n+7)/24.

A024868: a(n) = 2*(n+1) + 3*n + ... + (k+1)*(n+2-k), where k = [ n/2 ].

A029774: Digits of n^2 appear in n.

A035615: Number of winning length n strings with a 2 symbol alphabet in "same game".

A102150: a(0)=0; a(1)=2. Slowest increasing sequence where every digit "d" has a copy of itself in a(n+d).

A114166: Numbers n such that p(5n) is prime, where p(n) is the number of partitions of n.

A143554: G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^4.

A181373: Least m>0 such that prime(n) divides S(m)=A007908(m)=123...m and all numbers obtained by cyclic permutations of its digits; 0 if no such m exists.

A211183: Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 1, 3, 3, 6, 6, 10, 10, 15, ...) DELTA (1, 0, 2, 0, 3, 0, 4, 0, 5, ...) where DELTA is the operator defined in A084938.

A234508: 5*binomial(9*n+5,n)/(9*n+5).