Tuesday, April 6, 2021

Number of the day: 1244

Properties of the number 1244:

1244 = 22 × 311 is the 1040th composite number and is not squarefree.
1244 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 620 totatives.
1244 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 1244 results in a prime.
1244 = 3122 - 3102 is the difference of 2 nonnegative squares in 1 way.
1244 is the difference of 2 positive pentagonal numbers in 1 way.
1244 is not the sum of 3 positive squares.
12442 is the sum of 3 positive squares.
1244 is a proper divisor of 18672 - 1.
1244 is palindromic in (at least) the following bases: 12, 23, -20, and -27.
1244 in base 12 = 878 and consists of only the digits '7' and '8'.
1244 in base 22 = 2cc and consists of only the digits '2' and 'c'.
1244 in base 23 = 282 and consists of only the digits '2' and '8'.

The number 1244 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000025: Coefficients of the 3rd order mock theta function f(q).
A001749: Primes multiplied by 4.
A003368: Numbers that are the sum of 12 positive 6th powers.
A051226: Numbers m such that the Bernoulli number B_m has denominator 30.
A076042: a(0) = 0; thereafter a(n) = a(n-1) + n^2 if a(n-1) < n^2, otherwise a(n) = a(n-1) - n^2.
A085438: a(n) = Sum_{i=1..n} binomial(i+1,2)^3.
A098743: Number of partitions of n into aliquant parts (i.e., parts that do not divide n).
A126796: Number of complete partitions of n.
A292454: Numbers where 4 outnumbers any other digit.
A331683: One and all numbers of the form 2^k * prime(j) for k > 0 and j already in the sequence.

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