Tuesday, March 9, 2021

Number of the day: 334

Properties of the number 334:

334 = 2 × 167 is semiprime and squarefree.
334 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 166 totatives.
334 has a semiprime digit sum 10 in base 10.
334 has a triangular digit sum 10 in base 10.
334 has a triangular digit product 36 in base 10.
Reversing the decimal digits of 334 results in a prime.
334 is the difference of 2 positive pentagonal numbers in 2 ways.
334 = 32 + 102 + 152 is the sum of 3 positive squares.
3342 is the sum of 3 positive squares.
334 is a proper divisor of 16692 - 1.
334 = '33' + '4' is the concatenation of 2 semiprime numbers.
334 = '3' + '34' is the concatenation of 2 Fibonacci numbers.
334 is an emirpimes in (at least) the following bases: 3, 5, 9, 12, 13, 14, 15, 16, 17, 18, 19, 29, 32, 33, 34, 35, 37, 39, 41, 42, 45, 46, 49, 50, 55, 56, 57, 59, 60, 61, 63, 64, 67, 69, 71, 75, 84, 85, 86, 91, 92, 94, 97, and 100.
334 is palindromic in (at least) the following bases: -8, -10, and -37.
334 in base 3 = 110101 and consists of only the digits '0' and '1'.
334 in base 7 = 655 and consists of only the digits '5' and '6'.
334 in base 9 = 411 and consists of only the digits '1' and '4'.
334 consists of only the digits '3' and '4'.

The number 334 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000068: Numbers n such that n^4 + 1 is prime.
A003052: Self numbers or Colombian numbers (numbers that are not of the form m + sum of digits of m for any m).
A003278: Szekeres's sequence: a(n)-1 in ternary = n-1 in binary; also: a(1) = 1, a(2) = 2, and thereafter a(n) is smallest number k which avoids any 3-term arithmetic progression in a(1), a(2), ..., a(n-1), k.
A005237: Numbers n such that n and n+1 have the same number of divisors.
A005836: Numbers n whose base 3 representation contains no 2.
A100484: Even semiprimes.
A108917: Number of knapsack partitions of n.
A161344: Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
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.
A210000: Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n}.

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