Sunday, May 20, 2018

Number of the day: 71830

Properties of the number 71830:

71830 = 2 × 5 × 11 × 653 is the 64721th composite number and is squarefree.
71830 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 26080 totatives.
71830 has a prime digit sum 19 in base 10.
71830 = (167 × 168)/2 + … + (171 × 172)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
71830 is the sum of 2 positive triangular numbers.
71830 is the difference of 2 positive pentagonal numbers in 3 ways.
71830 = 102 + 212 + 2672 is the sum of 3 positive squares.
718302 = 430982 + 574642 = 100322 + 711262 = 295462 + 654722 = 346502 + 629202 is the sum of 2 positive squares in 4 ways.
718302 is the sum of 3 positive squares.
71830 is a proper divisor of 14920 - 1.
71830 is palindromic in (at least) base 84.

The number 71830 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A022314: a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0, a(1) = 9.

Saturday, May 19, 2018

Number of the day: 715257

Properties of the number 715257:

715257 = 33 × 59 × 449 is the 657564th composite number and is not squarefree.
715257 has 3 distinct prime factors, 16 divisors, 19 antidivisors and 467712 totatives.
715257 has an oblong digit product 2450 in base 10.
715257 = 3576292 - 3576282 = 1192112 - 1192082 = 397412 - 397322 = 132592 - 132322 = 60912 - 60322 = 21092 - 19322 = 10212 - 5722 = 9392 - 4082 is the difference of 2 nonnegative squares in 8 ways.
715257 is the sum of 2 positive triangular numbers.
715257 is the difference of 2 positive pentagonal numbers in 1 way.
715257 = 562 + 1152 + 8362 is the sum of 3 positive squares.
7152572 = 4460402 + 5591432 is the sum of 2 positive squares in 1 way.
7152572 is the sum of 3 positive squares.
715257 is a proper divisor of 188956 - 1.
715257 is palindromic in (at least) base 97.
715257 in base 3 = 1100100011000 and consists of only the digits '0' and '1'.
715257 in base 56 = 444P and consists of only the digits '4' and 'P'.

Friday, May 18, 2018

Number of the day: 58278

Bertrand Russell was born on this day 146 years ago.

Properties of the number 58278:

58278 = 2 × 3 × 11 × 883 is the 52375th composite number and is squarefree.
58278 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 17640 totatives.
58278 has a sphenic digit sum 30 in base 10.
58278 has an oblong digit sum 30 in base 10.
58278 is the sum of 2 positive triangular numbers.
58278 is the difference of 2 positive pentagonal numbers in 2 ways.
58278 = 12 + 142 + 2412 is the sum of 3 positive squares.
582782 is the sum of 3 positive squares.
58278 is a proper divisor of 14296 - 1.
58278 = '58' + '278' is the concatenation of 2 semiprime numbers.
58278 = '582' + '78' is the concatenation of 2 sphenic numbers.
58278 is palindromic in (at least) base 96.
58278 in base 21 = 6633 and consists of only the digits '3' and '6'.
58278 in base 39 = cCC and consists of only the digits 'C' and 'c'.

The number 58278 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A014531: Form array in which n-th row is obtained by expanding (1+x+x^2)^n and taking the 2nd column from the center.
A120906: Triangle read by rows: T(n,k) is the number of ternary words of length n on {0,1,2} having k drops (n>=0, k>=0). The drops of a ternary word on {0,1,2} are the subwords 10,20 and 21.
A227496: The Wiener index of the nanostar dendrimer defined pictorially as NS_3[n] in the Ashrafi et al. references.
A238875: Subdiagonal partitions: number of partitions (p1, p2, p3, ...) of n with pi <= i.
A291080: Irregular triangle read by rows: T(n,m) = number of lattice paths of type {A^H}_R terminating at point (n, m).

Thursday, May 17, 2018

Number of the day: 9673876020

Properties of the number 9673876020:

9673876020 = 22 × 3 × 5 × 161231267 is the 9232998162th composite number and is not squarefree.
9673876020 has 4 distinct prime factors, 24 divisors, 31 antidivisors and 2579700256 totatives.
9673876020 = 24184690062 - 24184690042 = 8061563382 - 8061563322 = 4836938062 - 4836937962 = 1612312822 - 1612312522 is the difference of 2 nonnegative squares in 4 ways.
9673876020 is the sum of 2 positive triangular numbers.
9673876020 is the difference of 2 positive pentagonal numbers in 2 ways.
9673876020 = 10282 + 11302 + 983442 is the sum of 3 positive squares.
96738760202 = 58043256122 + 77391008162 is the sum of 2 positive squares in 1 way.
96738760202 is the sum of 3 positive squares.
9673876020 is a proper divisor of 967940124 - 1.

Wednesday, May 16, 2018

Number of the day: 9123787746227

Pafnuty Lvovich Chebyshev was born on this day 197 years ago.

Properties of the number 9123787746227:

9123787746227 = 72 × 11 × 23 × 83 × 251 × 35327 is composite and not squarefree.
9123787746227 has 6 distinct prime factors, 96 divisors, 103 antidivisors and 6691450920000 totatives.
9123787746227 has a semiprime digit sum 65 in base 10.
9123787746227 is the difference of 2 nonnegative squares in 48 ways.
9123787746227 is the difference of 2 positive pentagonal numbers in 46 ways.
9123787746227 = 16772 + 102432 + 30205432 is the sum of 3 positive squares.
91237877462272 is the sum of 3 positive squares.
9123787746227 is a proper divisor of 4744728950 - 1.
9123787746227 = '9123787' + '746227' is the concatenation of 2 prime numbers.
9123787746227 = '9' + '123787746227' is the concatenation of 2 semiprime numbers.
9123787746227 = '91237877' + '46227' is the concatenation of 2 sphenic numbers.

Tuesday, May 15, 2018

Number of the day: 5193

Properties of the number 5193:

5193 = 32 × 577 is the 4501th composite number and is not squarefree.
5193 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 3456 totatives.
5193 = 43 + 63 + 173 is the sum of 3 positive cubes in 1 way.
5193 = 25972 - 25962 = 8672 - 8642 = 2932 - 2842 is the difference of 2 nonnegative squares in 3 ways.
5193 is the sum of 2 positive triangular numbers.
5193 is the difference of 2 positive pentagonal numbers in 1 way.
5193 = 32 + 722 is the sum of 2 positive squares in 1 way.
5193 = 22 + 172 + 702 is the sum of 3 positive squares.
51932 = 4322 + 51752 is the sum of 2 positive squares in 1 way.
51932 is the sum of 3 positive squares.
5193 is a proper divisor of 11532 - 1.
5193 = '5' + '193' is the concatenation of 2 prime numbers.
5193 = '51' + '93' is the concatenation of 2 emirpimes.
5193 is palindromic in (at least) the following bases: 24, 59, -20, -24, and -88.
5193 in base 8 = 12111 and consists of only the digits '1' and '2'.
5193 in base 23 = 9ii and consists of only the digits '9' and 'i'.
5193 in base 24 = 909 and consists of only the digits '0' and '9'.
5193 in base 41 = 33R and consists of only the digits '3' and 'R'.
5193 in base 58 = 1VV and consists of only the digits '1' and 'V'.
5193 in base 59 = 1T1 and consists of only the digits '1' and 'T'.

The number 5193 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024836: a(n) = least m such that if r and s in {1/1, 1/4, 1/7, ..., 1/(3n-2)} satisfy r < s, then r < k/m < (k+1)/m < s for some integer k.
A050065: a(n) = a(n-1)+a(m), where m=2^(p+1)+2-n and 2^p<n-1<=2^(p+1), for n >= 4.
A101853: a(n) = n*(20+15*n+n^2)/6.
A116646: Number of doubletons in all partitions of n. By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses).
A151793: Partial sums of A151782.
A179088: Positive integers of the form (2*m^2+1)/11.
A209814: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having two distinct values, and new values 0..3 introduced in row major order
A212417: Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> acb <--> bac where a<b<c.
A274160: Number of real integers in n-th generation of tree T(i) defined in Comments.
A288852: Number T(n,k) of matchings of size k in the triangle graph of order n; triangle T(n,k), n>=0, 0<=k<=floor(n*(n+1)/4), read by rows.

Monday, May 14, 2018

Number of the day: 467548

Properties of the number 467548:

467548 = 22 × 179 × 653 is the 428521th composite number and is not squarefree.
467548 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 232112 totatives.
467548 has a semiprime digit sum 34 in base 10.
467548 has a Fibonacci digit sum 34 in base 10.
467548 = 1168882 - 1168862 = 8322 - 4742 is the difference of 2 nonnegative squares in 2 ways.
467548 is the difference of 2 positive pentagonal numbers in 1 way.
467548 is not the sum of 3 positive squares.
4675482 = 2255402 + 4095522 is the sum of 2 positive squares in 1 way.
4675482 is the sum of 3 positive squares.
467548 is a proper divisor of 1433163 - 1.
467548 is palindromic in (at least) base -3.