Monday, September 24, 2018

Number of the day: 226

Gerolamo Cardano was born on this day 517 years ago.

Properties of the number 226:

226 = 2 × 113 is semiprime and squarefree.
226 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 112 totatives.
226 has a semiprime digit sum 10 in base 10.
226 has a triangular digit sum 10 in base 10.
226 has sum of divisors equal to 342 which is an oblong number.
Reversing the decimal digits of 226 results in an emirpimes.
226 is the sum of 2 positive triangular numbers.
226 is the difference of 2 positive pentagonal numbers in 2 ways.
226 = 12 + 152 is the sum of 2 positive squares in 1 way.
226 = 82 + 92 + 92 is the sum of 3 positive squares.
2262 = 302 + 2242 is the sum of 2 positive squares in 1 way.
2262 is the sum of 3 positive squares.
226 is a proper divisor of 6772 - 1.
226 = '22' + '6' is the concatenation of 2 semiprime numbers.
226 is an emirpimes in (at least) the following bases: 5, 6, 9, 10, 12, 13, 16, 19, 21, 22, 23, 24, 25, 27, 29, 35, 39, 41, 43, 51, 53, 55, 59, 62, 65, 66, 67, 71, 72, 73, 74, 78, 79, 81, 82, 84, 85, 89, 91, 92, 93, 94, 97, 98, and 100.
226 is palindromic in (at least) the following bases: 15, -14, -15, -25, -45, and -75.
226 in base 7 = 442 and consists of only the digits '2' and '4'.
226 consists of only the digits '2' and '6'.
226 in base 14 = 122 and consists of only the digits '1' and '2'.
226 in base 15 = 101 and consists of only the digits '0' and '1'.

The number 226 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002522: a(n) = n^2 + 1.
A005891: Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.
A006093: a(n) = prime(n) - 1.
A007770: Happy numbers: numbers whose trajectory under iteration of sum of squares of digits map (see A003132) includes 1.
A014486: List of totally balanced sequences of 2n binary digits written in base 10. Binary expansion of each term contains n 0's and n 1's and reading from left to right (the most significant to the least significant bit), the number of 0's never exceeds the number of 1's.
A016825: Positive integers congruent to 2 mod 4: a(n) = 4n+2, for n >= 0.
A016861: a(n) = 5*n + 1.
A031443: Digitally balanced numbers: numbers that in base 2 have the same number of 0's as 1's.
A100484: Even semiprimes.
A276625: Finitary numbers. Matula-Goebel numbers of rooted identity trees.

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