Tuesday, September 22, 2020

Number of the day: 550

Properties of the number 550:

550 = 2 × 52 × 11 is the 448th composite number and is not squarefree.
550 has 3 distinct prime factors, 12 divisors, 9 antidivisors and 200 totatives.
550 has a semiprime digit sum 10 in base 10.
550 has a triangular digit sum 10 in base 10.
550 = (4 × 5)/2 + … + (14 × 15)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
550 is the difference of 2 positive pentagonal numbers in 2 ways.
550 = 32 + 102 + 212 is the sum of 3 positive squares.
5502 = 3302 + 4402 = 1542 + 5282 is the sum of 2 positive squares in 2 ways.
5502 is the sum of 3 positive squares.
550 is a proper divisor of 1992 - 1.
550 = '55' + '0' is the concatenation of 2 triangular numbers.
550 = '55' + '0' is the concatenation of 2 Fibonacci numbers.
550 is palindromic in (at least) the following bases: 24, 49, 54, -13, and -61.
550 in base 7 = 1414 and consists of only the digits '1' and '4'.
550 consists of only the digits '0' and '5'.
550 in base 13 = 334 and consists of only the digits '3' and '4'.
550 in base 16 = 226 and consists of only the digits '2' and '6'.

The number 550 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002411: Pentagonal pyramidal numbers: a(n) = n^2*(n+1)/2.
A003349: Numbers that are the sum of 4 positive 5th powers.
A008593: Multiples of 11.
A028552: a(n) = n*(n+3).
A052224: Numbers whose sum of digits is 10.
A191113: Increasing sequence generated by these rules:a(1)=1, and if x is in a then 3x-2 and 4x-2 are in a.
A194368: Numbers n such that Sum_{k=1..n} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part.
A299281: Coordination sequence for "reo-e" 3D uniform tiling.
A306017: Number of non-isomorphic multiset partitions of weight n in which all parts have the same size.
A333218: Numbers k such that the k-th composition in standard order is a permutation (of an initial interval).

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