Saturday, September 15, 2018

Number of the day: 170

Properties of the number 170:

170 = 2 × 5 × 17 is a sphenic number and squarefree.
170 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 64 totatives.
170 has a Fibonacci digit sum 8 in base 10.
170 is the difference of 2 positive pentagonal numbers in 1 way.
170 = 72 + 112 = 12 + 132 is the sum of 2 positive squares in 2 ways.
170 = 52 + 82 + 92 is the sum of 3 positive squares.
1702 = 802 + 1502 = 262 + 1682 = 722 + 1542 = 1022 + 1362 is the sum of 2 positive squares in 4 ways.
1702 is the sum of 3 positive squares.
170 is a proper divisor of 1012 - 1.
170 = '1' + '70' is the concatenation of 2 pentagonal numbers.
170 is palindromic in (at least) the following bases: 4, 8, 13, 16, 33, 84, -12, and -13.
170 in base 3 = 20022 and consists of only the digits '0' and '2'.
170 in base 4 = 2222 and consists of only the digit '2'.
170 in base 6 = 442 and consists of only the digits '2' and '4'.
170 in base 7 = 332 and consists of only the digits '2' and '3'.
170 in base 8 = 252 and consists of only the digits '2' and '5'.
170 in base 12 = 122 and consists of only the digits '1' and '2'.
170 in base 13 = 101 and consists of only the digits '0' and '1'.

The number 170 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000096: a(n) = n*(n+3)/2.
A000404: Numbers that are the sum of 2 nonzero squares.
A000975: a(2n) = 2*a(2n-1), a(2n+1) = 2*a(2n)+1 (also a(n) is the n-th number without consecutive equal binary digits).
A001157: sigma_2(n): sum of squares of divisors of n.
A002522: a(n) = n^2 + 1.
A006218: a(n) = Sum_{k=1..n} floor(n/k); also Sum_{k=1..n} d(k), where d = number of divisors (A000005); also number of solutions to x*y = z with 1 <= x,y,z <= n.
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.
A014612: Numbers that are the product of exactly three (not necessarily distinct) primes.
A016825: Positive integers congruent to 2 mod 4: a(n) = 4n+2, for n >= 0.
A270339: Numbers n such that (11*10^n+19)/3 is prime.

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