Number of the day: 31109

Properties of the number 31109:

31109 = 13 × 2393 is semiprime and squarefree.
31109 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 28704 totatives.
31109 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 31109 results in an emirpimes.
31109 = 15555² - 15554² = 1203² - 1190² is the difference of 2 nonnegative squares in 2 ways.
31109 is the difference of 2 positive pentagonal numbers in 2 ways.
31109 = 47² + 170² = 22² + 175² is the sum of 2 positive squares in 2 ways.
31109 = 47² + 72² + 154² is the sum of 3 positive squares.
31109² = 7700² + 30141² = 4485² + 30784² = 15980² + 26691² = 11965² + 28716² is the sum of 2 positive squares in 4 ways.
31109² is the sum of 3 positive squares.
31109 is a proper divisor of 1279⁸ - 1.
31109 = '3' + '1109' is the concatenation of 2 prime numbers.
31109 is an emirpimes in (at least) the following bases: 2, 3, 5, 10, 11, 14, 17, 18, 19, 20, 22, 25, 28, 29, 31, 32, 34, 38, 40, 41, 42, 47, 51, 58, 65, 66, 69, 71, 73, 74, 77, 78, 81, 83, 85, 87, 91, 94, 97, 98, and 99.
31109 is palindromic in (at least) base -81.

The number 31109 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A009178: Expansion of cosh(x)*cosh(log(1+x)).
A056938: Concatenate all the prime divisors in previous term (with repetition), starting at 49.
A120884: (1/8)*number of lattice points with odd indices in a cubic lattice inside a sphere around the origin with radius 2*n.
A147466: Number of n X n binary arrays symmetric under 180 degree rotation with all ones connected only in a 1100-1111-0011 pattern in any orientation.
A148991: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, -1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}
A183899: Number of nondecreasing arrangements of n+3 numbers in 0..4 with each number being the sum mod 5 of three others
A186636: a(n) = n*(n^3+n^2+2*n+1).

Number of the day: 7219675

Properties of the number 7219675:

7219675 = 5² × 317 × 911 is the 6729112^th composite number and is not squarefree.
7219675 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 5751200 totatives.
7219675 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 7219675 results in a sphenic number.
7219675 = 3609838² - 3609837² = 721970² - 721965² = 144406² - 144381² = 11546² - 11229² = 4418² - 3507² = 3070² - 1485² is the difference of 2 nonnegative squares in 6 ways.
7219675 is the difference of 2 positive pentagonal numbers in 6 ways.
7219675 = 145² + 147² + 2679² is the sum of 3 positive squares.
7219675² = 4331805² + 5775740² = 2842320² + 6636635² = 4586885² + 5575320² = 1708125² + 7014700² = 2021509² + 6930888² = 324316² + 7212387² = 3603916² + 6255837² is the sum of 2 positive squares in 7 ways.
7219675² is the sum of 3 positive squares.
7219675 is a proper divisor of 1901⁹¹⁰ - 1.

Number of the day: 6282017

Henri Léon Lebesgue was born on this day 142 years ago.

Happy τ Day!

Properties of the number 6282017:

6282017 = 7 × 337 × 2663 is a sphenic number and squarefree.
6282017 has 3 distinct prime factors, 8 divisors, 31 antidivisors and 5366592 totatives.
6282017 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 6282017 results in a sphenic number.
6282017 = 3141009² - 3141008² = 448719² - 448712² = 9489² - 9152² = 2511² - 152² is the difference of 2 nonnegative squares in 4 ways.
6282017 is the difference of 2 positive pentagonal numbers in 3 ways.
6282017 = 43² + 142² + 2502² is the sum of 3 positive squares.
6282017² = 3262175² + 5368608² is the sum of 2 positive squares in 1 way.
6282017² is the sum of 3 positive squares.
6282017 is a proper divisor of 1523²³¹ - 1.
6282017 = '6' + '282017' is the concatenation of 2 semiprime numbers.

Number of the day: 2219

Properties of the number 2219:

2219 is a cyclic number.
2219 = 7 × 317 is semiprime and squarefree.
2219 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 1896 totatives.
2219 has a semiprime digit sum 14 in base 10.
2219 has a triangular digit product 36 in base 10.
Reversing the decimal digits of 2219 results in an emirpimes.
2219 = 1110² - 1109² = 162² - 155² is the difference of 2 nonnegative squares in 2 ways.
2219 is the difference of 2 positive pentagonal numbers in 2 ways.
2219 = 1² + 3² + 47² is the sum of 3 positive squares.
2219² = 525² + 2156² is the sum of 2 positive squares in 1 way.
2219² is the sum of 3 positive squares.
2219 is a proper divisor of 1471⁴ - 1.
2219 = '221' + '9' is the concatenation of 2 semiprime numbers.
2219 is an emirpimes in (at least) the following bases: 2, 4, 9, 10, 11, 12, 19, 21, 24, 28, 29, 34, 38, 40, 41, 42, 43, 45, 49, 51, 53, 62, 63, 69, 73, 76, 79, 80, 82, 83, 84, 85, 86, 93, 96, and 97.
2219 in base 23 = 44b and consists of only the digits '4' and 'b'.

The number 2219 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002212: Number of restricted hexagonal polyominoes with n cells.
A091965: Triangle read by rows: T(n,k)=number of lattice paths from (0,0) to (n,k) that do not go below the line y=0 and consist of steps U=(1,1), D=(1,-1) and three types of steps H=(1,0) (left factors of 3-Motzkin steps).
A112815: Numbers n such that 7*LCM(1,2,3,...,n) equals the denominator of the n-th harmonic number H(n).
A145812: Odd positive integers a(n) such that for every odd integer m>1 there exists a unique representation of m as a sum of the form a(l)+2a(s)
A213207: Number of distinct products i*j*k over all triples (i,j,k) with |i| + |j| + |k| <= n.
A216994: Multiples of 7 such that the digit sum is divisible by 7.
A226623: Irregular array read by rows in which row n lists the smallest elements, in ascending order, of conjecturally all primitive cycles of positive integers under iteration by the Collatz-like 3x-k function, where k = A226630(n).
A226627: Irregular array read by rows. a(n) is the smallest starting value of a T_k trajectory that includes A226623(n), where T_k is the Collatz-like 3x-k function associated with A226623(n).
A237341: For k in {2,3,...,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(4).
A259515: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0001 0101 0111

Number of the day: 5207010430

Properties of the number 5207010430:

5207010430 = 2 × 5 × 73 × 7132891 is the 4962794646^th composite number and is squarefree.
5207010430 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 2054272320 totatives.
5207010430 has a semiprime digit sum 22 in base 10.
5207010430 is the sum of 2 positive triangular numbers.
5207010430 is the difference of 2 positive pentagonal numbers in 4 ways.
5207010430 = 714² + 1145² + 72147² is the sum of 3 positive squares.
5207010430² = 3423787680² + 3923090050² = 385176114² + 5192744648² = 1084199432² + 5092884174² = 3124206258² + 4165608344² is the sum of 2 positive squares in 4 ways.
5207010430² is the sum of 3 positive squares.
5207010430 is a proper divisor of 941^1426578 - 1.

Number of the day: 30408

Properties of the number 30408:

30408 = 2³ × 3 × 7 × 181 is the 27122^th composite number and is not squarefree.
30408 has 4 distinct prime factors, 32 divisors, 11 antidivisors and 8640 totatives.
30408 has an emirpimes digit sum 15 in base 10.
30408 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 30408 results in a semiprime.
30408 = 7603² - 7601² = 3803² - 3799² = 2537² - 2531² = 1273² - 1261² = 1093² - 1079² = 557² - 529² = 383² - 341² = 223² - 139² is the difference of 2 nonnegative squares in 8 ways.
30408 is the sum of 2 positive triangular numbers.
30408 = 40² + 62² + 158² is the sum of 3 positive squares.
30408² = 3192² + 30240² is the sum of 2 positive squares in 1 way.
30408² is the sum of 3 positive squares.
30408 is a proper divisor of 743⁴ - 1.
30408 is palindromic in (at least) the following bases: 23, -36, -51, and -64.
30408 in base 19 = 4848 and consists of only the digits '4' and '8'.
30408 in base 23 = 2bb2 and consists of only the digits '2' and 'b'.
30408 in base 35 = oss and consists of only the digits 'o' and 's'.
30408 in base 50 = C88 and consists of only the digits '8' and 'C'.

The number 30408 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A097828: Partial sums of Chebyshev sequence S(n,13)= U(n,13/2)=A078362(n).
A111078: Concerning the popular MMORPG "Runescape" by JAGeX corporation, this sequence gives the number of experience points needed for a given level in a skill.
A141724: A triangle of coefficients of a double sum skew 4th level multinomial : t(n,m,k,l)=Sum[Sum[Multinomial[n - m - k - l, m, k, l], {l, 0, k}], {k, 0, m}].
A277631: Number of aperiodic necklaces (Lyndon words) with k<=6 black beads and n-k white beads.
A288564: Number of connected one-sided arrangements of n pseudo-circles in the affine plane, in the sense that the union of the solid pseudo-circles is a connected set.

Number of the day: 7170

Properties of the number 7170:

7170 = 2 × 3 × 5 × 239 is the 6253^th composite number and is squarefree.
7170 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 1904 totatives.
7170 has an emirpimes digit sum 15 in base 10.
7170 has a triangular digit sum 15 in base 10.
7170 is the difference of 2 positive pentagonal numbers in 2 ways.
7170 = 5² + 16² + 83² is the sum of 3 positive squares.
7170² = 4302² + 5736² is the sum of 2 positive squares in 1 way.
7170² is the sum of 3 positive squares.
7170 is a proper divisor of 479² - 1.
7170 is palindromic in (at least) the following bases: 14, 56, 67, -36, and -64.
7170 in base 7 = 26622 and consists of only the digits '2' and '6'.
7170 in base 14 = 2882 and consists of only the digits '2' and '8'.
7170 in base 25 = bbk and consists of only the digits 'b' and 'k'.
7170 in base 34 = 66u and consists of only the digits '6' and 'u'.
7170 in base 55 = 2KK and consists of only the digits '2' and 'K'.
7170 in base 56 = 2G2 and consists of only the digits '2' and 'G'.

The number 7170 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A054341: Row sums of triangle A054336 (central binomial convolutions).
A055574: n satisfying sigma(n+1) = sigma(n-1).
A067347: Square array read by antidiagonals: T(n,k)=(T(n,k-1)*n^2-Catalan(k-1)*n)/(n-1) with a(n,0)=1 and a(1,k)=Catalan(k) where Catalan(k)=C(2k,k)/(k+1)=A000108(k).
A076036: G.f.: 1/(1 - 5*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.
A125205: Triangular array T(n,k) (n>=1, 0<=k<=n(n-1)/2) giving the total number of connected components in all subgraphs (V,E') with |E'|=k of the complete labeled graph K_n=(V,E).
A125206: Triangular array T(n,k) (n>=1, 0<=k<=n(n-1)/2) giving the total number of connected components in all subgraphs obtained from the complete labeled graph K_n by removing k edges.
A139274: a(n) = n*(8*n-1).
A239832: Number of partitions of n having 1 more even part than odd, so that there is an ordering of parts for which the even and odd parts alternate and the first and last terms are even.
A240192: T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4
A269467: T(n,k)=Number of length-n 0..k arrays with no repeated value equal to the previous repeated value.