## Stefan Banach was born on this day 125 years ago.

### Properties of the number 3553:

3553 = 11 × 17 × 19 is a sphenic number and squarefree.3553 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 2880 totatives.

3553 = 1777

^{2}- 1776

^{2}= 167

^{2}- 156

^{2}= 113

^{2}- 96

^{2}= 103

^{2}- 84

^{2}is the difference of 2 nonnegative squares in 4 ways.

3553 is the sum of 2 positive triangular numbers.

3553 is the difference of 2 positive pentagonal numbers in 4 ways.

3553 = 15

^{2}+ 32

^{2}+ 48

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

3553

^{2}= 1672

^{2}+ 3135

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

3553

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

3553 is a divisor of 647

^{5}- 1.

3553 is a palindrome (in base 10).

3553 is palindromic in (at least) the following bases: 48, -53, -74, and -96.

3553 in base 3 = 11212121 and consists of only the digits '1' and '2'.

3553 in base 9 = 4777 and consists of only the digits '4' and '7'.

3553 consists of only the digits '3' and '5'.

3553 in base 22 = 77b and consists of only the digits '7' and 'b'.

3553 in base 47 = 1SS and consists of only the digits '1' and 'S'.

3553 in base 48 = 1Q1 and consists of only the digits '1' and 'Q'.

3553 in base 59 = 11D and consists of only the digits '1' and 'D'.

### The number 3553 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A000566: Heptagonal numbers (or 7-gonal numbers): n(5n-3)/2.

A023548: Convolution of natural numbers >= 2 and Fibonacci numbers.

A056524: Palindromes with even number of digits.

A059820: Expansion of series related to Liouville's Last Theorem: g.f. sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^3 *product_{i=1..t} (1-x^i) ).

A080859: a(n) = 6*n^2 + 4*n + 1.

A083832: Palindromes of the form 4n + 1 where n is also a palindrome. Palindromes arising in A083831.

A131423: a(n) = n*(n+2)*(2*n-1)/3. Also, row sums of triangle A131422.

A152942: Odd squarefree numbers n such that the cyclotomic polynomial Phi(n,x) has height 4.

A182269: Number of representations of n as a sum of products of pairs of positive integers, considered to be equivalent when terms or factors are reordered.

A255159: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with no 3x3 subblock diagonal sum 1 and no antidiagonal sum 1 and no row sum 0 or 1 and no column sum 0 or 1

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