Tuesday, June 27, 2017

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

Monday, June 26, 2017

Number of the day: 5207010430

Properties of the number 5207010430:

5207010430 = 2 × 5 × 73 × 7132891 is the 4962794646th 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 9411426578 - 1.

Sunday, June 25, 2017

Number of the day: 30408

Properties of the number 30408:

30408 = 23 × 3 × 7 × 181 is the 27122th 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.

Saturday, June 24, 2017

Number of the day: 7170

Properties of the number 7170:

7170 = 2 × 3 × 5 × 239 is the 6253th 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.

Thursday, June 22, 2017

Number of the day: 1509

Hermann Minkowski was born on this day 153 years ago.

Properties of the number 1509:

1509 is a cyclic number.
1509 = 3 × 503 is semiprime and squarefree.
1509 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 1004 totatives.
1509 has an emirpimes digit sum 15 in base 10.
1509 has a triangular digit sum 15 in base 10.
1509 has sum of divisors equal to 2016 which is a triangular number.
Reversing the decimal digits of 1509 results in a sphenic number.
1509 = 7552 - 7542 = 2532 - 2502 is the difference of 2 nonnegative squares in 2 ways.
1509 is the sum of 2 positive triangular numbers.
1509 is the difference of 2 positive pentagonal numbers in 1 way.
1509 = 82 + 172 + 342 is the sum of 3 positive squares.
15092 is the sum of 3 positive squares.
1509 is a proper divisor of 7251 - 1.
1509 is an emirpimes in (at least) the following bases: 4, 6, 9, 11, 12, 15, 18, 19, 20, 22, 24, 32, 36, 38, 41, 42, 47, 49, 55, 57, 59, 60, 64, 65, 71, 75, 77, 83, 84, 87, 91, 93, 96, 98, and 99.
1509 is palindromic in (at least) the following bases: 16, 29, -52, and -58.
1509 in base 16 = 5e5 and consists of only the digits '5' and 'e'.
1509 in base 28 = 1pp and consists of only the digits '1' and 'p'.
1509 in base 29 = 1n1 and consists of only the digits '1' and 'n'.
1509 in base 38 = 11R and consists of only the digits '1' and 'R'.

The number 1509 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005228: Sequence and first differences (A030124) together list all positive numbers exactly once.
A006832: Discriminants of totally real cubic fields.
A026105: Triangle T read by rows: differences of Motzkin triangle (A026300).
A059993: Pinwheel numbers: a(n) = 2*n^2 + 6*n + 1.
A094612: Fundamental discriminants of real quadratic number fields with class number 3.
A165652: Number of disconnected 2-regular graphs on n vertices.
A202124: T(n,k)=Number of -k..k arrays of n elements with first, second and third differences also in -k..k
A224146: T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing
A241306: 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 zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4
A279567: Number of length n inversion sequences avoiding the patterns 100, 110, 120, and 210.

Wednesday, June 21, 2017

Number of the day: 9348

Properties of the number 9348:

9348 = 22 × 3 × 19 × 41 is the 8190th composite number and is not squarefree.
9348 has 4 distinct prime factors, 24 divisors, 11 antidivisors and 2880 totatives.
Reversing the decimal digits of 9348 results in a sphenic number.
9348 = 23382 - 23362 = 7822 - 7762 = 1422 - 1042 = 982 - 162 is the difference of 2 nonnegative squares in 4 ways.
9348 is the sum of 2 positive triangular numbers.
9348 is the difference of 2 positive pentagonal numbers in 1 way.
9348 = 22 + 402 + 882 is the sum of 3 positive squares.
93482 = 20522 + 91202 is the sum of 2 positive squares in 1 way.
93482 is the sum of 3 positive squares.
9348 is a proper divisor of 15592 - 1.
9348 is palindromic in (at least) the following bases: -13, -22, -26, and -33.
9348 in base 25 = enn and consists of only the digits 'e' and 'n'.
9348 in base 32 = 944 and consists of only the digits '4' and '9'.
9348 in base 36 = 77o and consists of only the digits '7' and 'o'.

The number 9348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001610: a(n) = a(n-1) + a(n-2) + 1.
A031367: Inflation orbit counts.
A099925: a(n) = Lucas(n) + (-1)^n.
A120019: Square table, read by antidiagonals, of self-compositions of A120010.
A120020: Coefficients of x^n in the n-th iteration of the g.f. of A120010: a(n) = [x^n] { (1-sqrt(1-4*x))/2 o x/(1-n*x) o (x-x^2) } for n>=1.
A179249: Numbers n that have 9 terms in their Zeckendorf representation.
A197218: Phi(Lucas(n)).
A209796: T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly one duplicate clockwise edge difference
A214980: Positions of zeros in A214979.
A231089: Initial members of abundant quadruplets, i.e., values of n such that (n, n+2, n+4, n+6) are all abundant numbers.

Tuesday, June 20, 2017

Number of the day: 746010

Properties of the number 746010:

746010 = 2 × 35 × 5 × 307 is the 686066th composite number and is not squarefree.
746010 has 4 distinct prime factors, 48 divisors, 25 antidivisors and 198288 totatives.
746010 = 203 + 433 + 873 = 423 + 633 + 753 is the sum of 3 positive cubes in 2 ways.
746010 is the difference of 2 positive pentagonal numbers in 1 way.
746010 = 552 + 1242 + 8532 is the sum of 3 positive squares.
7460102 = 4476062 + 5968082 is the sum of 2 positive squares in 1 way.
7460102 is the sum of 3 positive squares.
746010 is a proper divisor of 63127 - 1.
746010 is palindromic in (at least) base -97.