Monday, July 27, 2020

Number of the day: 4918

Properties of the number 4918:

4918 is the 1241th totient number.
4918 = 2 × 2459 is semiprime and squarefree.
4918 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 2458 totatives.
4918 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 4918 results in a sphenic number.
4918 is the difference of 2 positive pentagonal numbers in 2 ways.
4918 = 62 + 112 + 692 is the sum of 3 positive squares.
49182 is the sum of 3 positive squares.
4918 is a proper divisor of 31229 - 1.
4918 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 8, 11, 14, 15, 16, 19, 21, 23, 26, 29, 30, 33, 35, 37, 40, 45, 50, 51, 52, 54, 56, 60, 65, 70, 71, 73, 74, 79, 80, 87, 89, 97, 98, and 100.
4918 is palindromic in (at least) the following bases: -4, and -39.
4918 in base 6 = 34434 and consists of only the digits '3' and '4'.
4918 in base 9 = 6664 and consists of only the digits '4' and '6'.
4918 in base 26 = 774 and consists of only the digits '4' and '7'.
4918 in base 49 = 22I and consists of only the digits '2' and 'I'.

The number 4918 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006137: a(n) = 1 + n/2 + 9*n^2/2.
A084381: a(n) = n^3 + 5.
A089395: Prime productive numbers n: Let the digits of n be abcd. Then the numbers bcd*a+1, cd*ab+1, d*abc+1, abcd+1 etc. are all primes. If n is a k-digit number it produces k such primes.
A099411: Numbers n such that 3*R_n + 4 is prime, where R_n = 11...1 is the repunit (A002275) of length n.
A168011: a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2.
A194593: Semiprimes s such that phi(s)/2 is prime.
A204662: Numbers n such that n!8-1 is prime.
A211650: Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^3 < x^3 + y^3.
A215431: Numbers n such that n^128+(n+1)^128 is a prime.
A285799: Number of partitions of n into parts with an odd number of distinct prime divisors.

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