Wednesday, August 24, 2016

Number of the day: 3548

Properties of the number 3548:

3548 = 22 × 887 is the 3050th composite number and is not squarefree.
3548 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 1772 totatives.
3548 has an oblong digit sum 20 in base 10.
3548 has sum of divisors equal to 6216 which is a triangular number.
Reversing the decimal digits of 3548 results in a semiprime.
3548 = 8882 - 8862 is the difference of 2 nonnegative squares in 1 way.
3548 is the difference of 2 positive pentagonal numbers in 1 way.
3548 is not the sum of 3 positive squares.
35482 is the sum of 3 positive squares.
3548 is a divisor of 13443 - 1.
3548 is palindromic in (at least) the following bases: 17, 20, and 23.
3548 in base 16 = ddc and consists of only the digits 'c' and 'd'.
3548 in base 17 = c4c and consists of only the digits '4' and 'c'.
3548 in base 20 = 8h8 and consists of only the digits '8' and 'h'.
3548 in base 22 = 776 and consists of only the digits '6' and '7'.
3548 in base 23 = 6g6 and consists of only the digits '6' and 'g'.
3548 in base 59 = 118 and consists of only the digits '1' and '8'.

The number 3548 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000954: Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.
A008509: Numbers n such that n-th triangular number is palindromic.
A053618: a(n) = ceiling(C(n,4)/n).
A066321: Binary representation of base i-1 expansion of n: replace i-1 by 2 in base i-1 expansion of n.
A127764: Integer part of Gauss' Arithmetic-Geometric Mean M(2,n^3).
A234500: Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
A245173: Triangle read by rows: coefficients of the polynomials A_{3,4}(n,k).
A252993: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly 2 distinct values, in every diagonal 1 or 2 distinct values, in every antidiagonal 2 or 3 distinct values, and new values 0 upwards introduced in row major order
A261761: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column prime, read as a binary number with top and left being the most significant bits.
A270980: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 237", based on the 5-celled von Neumann neighborhood.

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