Number of the day: 2613

Niels Henrik Abel was born on this day 220 years ago.

Properties of the number 2613:

2613 = 3 × 13 × 67 is a sphenic number and squarefree.
2613 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 1584 totatives.
2613 has an oblong digit sum 12 in base 10.
2613 has a triangular digit product 36 in base 10.
2613 = 1307² - 1306² = 437² - 434² = 107² - 94² = 53² - 14² is the difference of 2 nonnegative squares in 4 ways.
2613 is the sum of 2 positive triangular numbers.
2613 is the difference of 2 positive pentagonal numbers in 2 ways.
2613 = 7² + 8² + 50² is the sum of 3 positive squares.
2613² = 1005² + 2412² is the sum of 2 positive squares in 1 way.
2613² is the sum of 3 positive squares.
2613 is a proper divisor of 937² - 1.
2613 = '2' + '613' is the concatenation of 2 prime numbers.
2613 is palindromic in (at least) the following bases: 29, 66, and -30.
2613 in base 25 = 44d and consists of only the digits '4' and 'd'.
2613 in base 28 = 399 and consists of only the digits '3' and '9'.
2613 in base 29 = 333 and consists of only the digit '3'.

The number 2613 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022288: a(n) = n*(31*n-1)/2.
A121033: Multiples of 13 containing a 13 in their decimal representation.
A130689: Number of partitions of n such that every part divides the largest part; a(0) = 1.
A140674: a(n) = n*(3*n + 17)/2.
A153875: 3 times 13-gonal (or tridecagonal) numbers: 3*n*(11*n - 9)/2.
A209032: T(n,k) is the number of n-bead necklaces labeled with numbers -k..k allowing reversal, with sum zero and first differences in -k..k.
A231855: T(n,k)=Number of nXk 0..2 arrays with no element having a strict majority of its horizontal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions)
A244788: T(n,k)=Number of length n 0..k arrays with each partial sum starting from the beginning no more than one standard deviation from its mean.
A349053: Number of non-weakly alternating integer compositions of n.
A350844: Number of strict integer partitions of n with no difference -2.