Tuesday, December 12, 2017

Number of the day: 732499

Properties of the number 732499:

732499 is a cyclic number.
732499 = 31 × 23629 is semiprime and squarefree.
732499 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 708840 totatives.
732499 has a semiprime digit sum 34 in base 10.
732499 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 732499 results in a prime.
732499 = 3662502 - 3662492 = 118302 - 117992 is the difference of 2 nonnegative squares in 2 ways.
732499 is the difference of 2 positive pentagonal numbers in 2 ways.
732499 = 332 + 1032 + 8492 is the sum of 3 positive squares.
7324992 = 874512 + 7272602 is the sum of 2 positive squares in 1 way.
7324992 is the sum of 3 positive squares.
732499 is a proper divisor of 1373660 - 1.
732499 = '73249' + '9' is the concatenation of 2 semiprime numbers.
732499 is an emirpimes in (at least) the following bases: 3, 4, 7, 8, 13, 16, 17, 22, 28, 29, 33, 35, 38, 39, 41, 49, 50, 58, 60, 62, 63, 66, 67, 68, 69, 73, 74, 77, 79, 80, 82, 83, 89, 90, 91, 96, and 100.
732499 is palindromic in (at least) the following bases: 26, and -92.
732499 in base 5 = 141414444 and consists of only the digits '1' and '4'.

Monday, December 11, 2017

Number of the day: 892849

Properties of the number 892849:

892849 is a cyclic number.
892849 is the 70763th prime.
892849 has 13 antidivisors and 892848 totatives.
Reversing the decimal digits of 892849 results in a sphenic number.
892849 = 4464252 - 4464242 is the difference of 2 nonnegative squares in 1 way.
892849 is the sum of 2 positive triangular numbers.
892849 is the difference of 2 positive pentagonal numbers in 1 way.
892849 = 602 + 9432 is the sum of 2 positive squares in 1 way.
892849 = 2182 + 3872 + 8342 is the sum of 3 positive squares.
8928492 = 1131602 + 8856492 is the sum of 2 positive squares in 1 way.
8928492 is the sum of 3 positive squares.
892849 is a proper divisor of 1741979 - 1.
892849 is an emirp in (at least) the following bases: 5, 13, 14, 15, 22, 25, 28, 29, 40, 59, 75, 81, 86, and 99.

Sunday, December 10, 2017

Number of the day: 77679

Carl Gustav Jacob Jacobi was born on this day 213 years ago.

Properties of the number 77679:

77679 = 34 × 7 × 137 is the 70046th composite number and is not squarefree.
77679 has 3 distinct prime factors, 20 divisors, 23 antidivisors and 44064 totatives.
77679 has a triangular digit sum 36 in base 10.
77679 = 63 + 153 + 423 is the sum of 3 positive cubes in 1 way.
77679 is the difference of 2 nonnegative squares in 10 ways.
77679 is the difference of 2 positive pentagonal numbers in 1 way.
77679 is not the sum of 3 positive squares.
776792 = 498962 + 595352 is the sum of 2 positive squares in 1 way.
776792 is the sum of 3 positive squares.
77679 is a proper divisor of 109718 - 1.
77679 = '77' + '679' is the concatenation of 2 semiprime numbers.
77679 is palindromic in (at least) the following bases: 47, 90, and -54.
77679 in base 47 = Z7Z and consists of only the digits '7' and 'Z'.
77679 in base 53 = RYY and consists of only the digits 'R' and 'Y'.

The number 77679 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A211545: Number of ordered triples (w,x,y) with all terms in {-n,...-1,1,...,n} and w+x+y>0.
A274361: Numbers n such that n and n+1 both have 20 divisors.
A293440: First differences of A293230: how many more alive nodes there are in generation n+1 than in generation n in the binary tree of persistently squarefree numbers.

Saturday, December 9, 2017

Number of the day: 4815

Properties of the number 4815:

4815 = 32 × 5 × 107 is the 4166th composite number and is not squarefree.
4815 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 2544 totatives.
4815 = 292 + … + 332 is the sum of at least 2 consecutive positive squares in 1 way.
4815 = 73 + 123 + 143 is the sum of 3 positive cubes in 1 way.
4815 = 24082 - 24072 = 8042 - 8012 = 4842 - 4792 = 2722 - 2632 = 1682 - 1532 = 762 - 312 is the difference of 2 nonnegative squares in 6 ways.
4815 is the difference of 2 positive pentagonal numbers in 1 way.
4815 is not the sum of 3 positive squares.
48152 = 28892 + 38522 is the sum of 2 positive squares in 1 way.
48152 is the sum of 3 positive squares.
4815 is a proper divisor of 6416 - 1.
4815 = '4' + '815' is the concatenation of 2 semiprime numbers.
4815 is palindromic in (at least) the following bases: 6, 58, and -83.
4815 in base 24 = 88f and consists of only the digits '8' and 'f'.
4815 in base 57 = 1RR and consists of only the digits '1' and 'R'.
4815 in base 58 = 1P1 and consists of only the digits '1' and 'P'.

The number 4815 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001522: Number of n-stacks with strictly receding walls, or planar partitions of n.
A027578: Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
A051865: 13-gonal (or tridecagonal) numbers: a(n) = n*(11*n - 9)/2.
A090669: Numbers n such that 7^n - 2 is a prime.
A121035: Multiples of 15 containing a 15 in their decimal representation.
A131246: Row sums of triangle A131245.
A226514: Column 3 of array in A226513.
A238128: Triangle read by rows: T(n,k) gives the number of ballot sequences of length n having largest descent k, n>=0, 0<=k<=n.
A257211: Numbers n such that the decimal expansions of both n and n^2 have 1 as smallest digit and 8 as largest digit.
A275172: Positions of 3 in A274640.

Friday, December 8, 2017

Number of the day: 429203302

Jacques Salomon Hadamard was born on this day 152 years ago.

Julia Robinson was born on this day 98 years ago.

Properties of the number 429203302:

429203302 = 2 × 11 × 19509241 is a sphenic number and squarefree.
429203302 has 3 distinct prime factors, 8 divisors, 39 antidivisors and 195092400 totatives.
429203302 has a semiprime digit sum 25 in base 10.
429203302 is the sum of 2 positive triangular numbers.
429203302 is the difference of 2 positive pentagonal numbers in 2 ways.
429203302 = 862 + 2912 + 207152 is the sum of 3 positive squares.
4292033022 = 3014441982 + 3055272002 is the sum of 2 positive squares in 1 way.
4292033022 is the sum of 3 positive squares.
429203302 is a proper divisor of 683162577 - 1.
429203302 = '429203' + '302' is the concatenation of 2 semiprime numbers.
429203302 = '42' + '9203302' is the concatenation of 2 sphenic numbers.

Thursday, December 7, 2017

Number of the day: 696787

Properties of the number 696787:

696787 = 7 × 132 × 19 × 31 is the 640473th composite number and is not squarefree.
696787 has 4 distinct prime factors, 24 divisors, 47 antidivisors and 505440 totatives.
696787 has a prime digit sum 43 in base 10.
696787 = 833 + 503 is the sum of 2 positive cubes in 1 way.
696787 is the difference of 2 nonnegative squares in 12 ways.
696787 is the sum of 2 positive triangular numbers.
696787 is the difference of 2 positive pentagonal numbers in 12 ways.
696787 = 392 + 1212 + 8252 is the sum of 3 positive squares.
6967872 = 2679952 + 6431882 = 4906372 + 4947602 is the sum of 2 positive squares in 2 ways.
6967872 is the sum of 3 positive squares.
696787 is a proper divisor of 1913 - 1.
696787 = '69' + '6787' is the concatenation of 2 semiprime numbers.

The number 696787 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001872: Convolved Fibonacci numbers.
A061179: Fourth column (m=3) of triangle A060920 (bisection of Fibonacci triangle, even part).
A163763: Sqrt(sigma(A008847(n)^2)), where A008847 lists m such that sigma(m^2) is a square.

Wednesday, December 6, 2017

Number of the day: 1666

Properties of the number 1666:

1666 = 2 × 72 × 17 is the 1404th composite number and is not squarefree.
1666 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 672 totatives.
1666 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 1666 results in a prime.
1666 is the difference of 2 positive pentagonal numbers in 4 ways.
1666 = 212 + 352 is the sum of 2 positive squares in 1 way.
1666 = 12 + 242 + 332 is the sum of 3 positive squares.
16662 = 7842 + 14702 is the sum of 2 positive squares in 1 way.
16662 is the sum of 3 positive squares.
1666 is a proper divisor of 8832 - 1.
1666 = '166' + '6' is the concatenation of 2 semiprime numbers.
1666 = '1' + '666' is the concatenation of 2 triangular numbers.
1666 is palindromic in (at least) the following bases: 26, 37, 48, 97, -32, and -45.
1666 in base 6 = 11414 and consists of only the digits '1' and '4'.
1666 consists of only the digits '1' and '6'.
1666 in base 23 = 33a and consists of only the digits '3' and 'a'.
1666 in base 25 = 2gg and consists of only the digits '2' and 'g'.
1666 in base 26 = 2c2 and consists of only the digits '2' and 'c'.
1666 in base 36 = 1aa and consists of only the digits '1' and 'a'.
1666 in base 37 = 181 and consists of only the digits '1' and '8'.
1666 in base 40 = 11Q and consists of only the digits '1' and 'Q'.

The number 1666 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026798: Number of partitions of n in which the least part is 5.
A033547: Otto Haxel's guess for magic numbers of nuclear shells.
A035607: Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d>=1, m >= 0).
A054252: Triangle T(n,k) of n X n binary matrices with k=0..n^2 ones under action of dihedral group of the square D_4.
A132760: a(n) = n(n+15).
A145540: Number of numbers removed in each step of Eratosthenes' sieve for 10^4.
A185325: Number of partitions of n into parts >= 5.
A191726: Dispersion of A047216, (numbers >1 and congruent to 1 or 2 mod 5), by antidiagonals.
A195313: Generalized 13-gonal numbers: n*(11*n-9)/2, n=0,1,-1,2,-2,...
A292456: Numbers where 6 outnumbers any other digit.