Thursday, May 19, 2016

Number of the day: 3439

Properties of the number 3439:

3439 = 19 × 181 is semiprime and squarefree.
3439 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 3240 totatives.
3439 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 3439 results in a prime.
3439 = 153 + 43 is the sum of 2 positive cubes in 1 way.
3439 = 17202 - 17192 = 1002 - 812 is the difference of 2 nonnegative squares in 2 ways.
3439 is the sum of 2 positive triangular numbers.
3439 is the difference of 2 positive pentagonal numbers in 2 ways.
3439 is not the sum of 3 positive squares.
34392 = 3612 + 34202 is the sum of 2 positive squares in 1 way.
34392 is the sum of 3 positive squares.
3439 is a divisor of 2293 - 1.
3439 = '3' + '439' is the concatenation of 2 prime numbers.
3439 = '34' + '39' is the concatenation of 2 semiprime numbers.
3439 is an emirpimes in (at least) the following bases: 3, 4, 9, 11, 13, 16, 17, 24, 25, 27, 29, 31, 37, 41, 42, 43, 44, 45, 46, 47, 50, 51, 52, 57, 62, 66, 70, 71, 80, 81, 83, 88, 89, 91, 93, 95, 96, 97, 98, and 99.
3439 is palindromic in (at least) base 22.
3439 in base 21 = 7gg and consists of only the digits '7' and 'g'.
3439 in base 22 = 727 and consists of only the digits '2' and '7'.
3439 in base 58 = 11H and consists of only the digits '1' and 'H'.

The number 3439 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005917: Rhombic dodecahedral numbers: n^4 - (n-1)^4.
A006003: a(n) = n*(n^2 + 1)/2.
A016189: a(n) = 10^n - 9^n.
A051874: 22-gonal numbers: a(n) = n*(10*n-9).
A074149: Sum of terms in each group in A074147.
A147857: Differences of two positive 4th powers.
A222182: Numbers m such that 2m+11 is a square.
A226929: Values of n such that L(9) and N(9) are both prime, where L(k) = (n^2+n+1)*2^(2*k) + (2*n+1)*2^k + 1, N(k) = (n^2+n+1)*2^k + n.
A228644: Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=7.
A250477: Number of times prime(n) (the n-th prime) occurs as the least prime factor among numbers 1 .. (prime(n)^2 * prime(n+1)): a(n) = A078898(A251720(n)).

No comments:

Post a Comment