Sunday, February 25, 2018

Number of the day: 992267

Properties of the number 992267:

992267 is a cyclic number.
992267 and 992269 form a twin prime pair.
992267 has 13 antidivisors and 992266 totatives.
992267 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 992267 results in a sphenic number.
992267 = 4961342 - 4961332 is the difference of 2 nonnegative squares in 1 way.
992267 is the difference of 2 positive pentagonal numbers in 1 way.
992267 = 172 + 772 + 9932 is the sum of 3 positive squares.
9922672 is the sum of 3 positive squares.
992267 is a proper divisor of 14391219 - 1.
992267 is an emirp in (at least) the following bases: 2, 5, 15, 27, 35, 41, 50, 77, 82, 84, 86, 87, 88, 91, and 94.

The number 992267 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A188273: Number of nondecreasing strings of numbers x(i=1..n) in -5..5 with sum x(i)^3 equal to 0.

Saturday, February 24, 2018

Number of the day: 112779

Properties of the number 112779:

112779 = 33 × 4177 is the 102095th composite number and is not squarefree.
112779 has 2 distinct prime factors, 8 divisors, 11 antidivisors and 75168 totatives.
112779 = 563902 - 563892 = 187982 - 187952 = 62702 - 62612 = 21022 - 20752 is the difference of 2 nonnegative squares in 4 ways.
112779 is the difference of 2 positive pentagonal numbers in 1 way.
112779 = 52 + 232 + 3352 is the sum of 3 positive squares.
1127792 = 311042 + 1084052 is the sum of 2 positive squares in 1 way.
1127792 is the sum of 3 positive squares.
112779 is a proper divisor of 15118 - 1.
112779 in base 51 = hII and consists of only the digits 'I' and 'h'.

Friday, February 23, 2018

Number of the day: 574421601

Properties of the number 574421601:

574421601 = 3 × 13 × 113 × 130343 is the 544364034th composite number and is squarefree.
574421601 has 4 distinct prime factors, 16 divisors, 29 antidivisors and 350359296 totatives.
574421601 has a sphenic digit sum 30 in base 10.
574421601 has an oblong digit sum 30 in base 10.
574421601 = 2872108012 - 2872108002 = 957369352 - 957369322 = 220931452 - 220931322 = 73643992 - 73643602 = 25417452 - 25416322 = 8473992 - 8470602 = 1962492 - 1947802 = 673752 - 629682 is the difference of 2 nonnegative squares in 8 ways.
574421601 is the difference of 2 positive pentagonal numbers in 4 ways.
574421601 = 112 + 4942 + 239622 is the sum of 3 positive squares.
5744216012 = 1485910202 + 5548701512 = 762506552 + 5693382242 = 2893614602 + 4962158012 = 2209313852 + 5302353242 is the sum of 2 positive squares in 4 ways.
5744216012 is the sum of 3 positive squares.
574421601 is a proper divisor of 677130342 - 1.

Thursday, February 22, 2018

Number of the day: 630919

Frank Plumpton Ramsey was born on this day 115 years ago.

Properties of the number 630919:

630919 is a cyclic number.
630919 is the 51405th prime.
630919 has 3 antidivisors and 630918 totatives.
630919 has a triangular digit sum 28 in base 10.
630919 = 3154602 - 3154592 is the difference of 2 nonnegative squares in 1 way.
630919 is the sum of 2 positive triangular numbers.
630919 is the difference of 2 positive pentagonal numbers in 1 way.
630919 is not the sum of 3 positive squares.
6309192 is the sum of 3 positive squares.
630919 is a proper divisor of 22735051 - 1.
630919 = '63091' + '9' is the concatenation of 2 semiprime numbers.
630919 is an emirp in (at least) the following bases: 9, 13, 14, 25, 30, 32, 36, 39, 51, 53, 63, 65, 67, 77, 82, 87, and 97.
630919 is palindromic in (at least) base -92.

Wednesday, February 21, 2018

Number of the day: 73348

Properties of the number 73348:

73348 = 22 × 11 × 1667 is the 66104th composite number and is not squarefree.
73348 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 33320 totatives.
73348 has a semiprime digit sum 25 in base 10.
73348 has a triangular digit product 2016 in base 10.
73348 = 183382 - 183362 = 16782 - 16562 is the difference of 2 nonnegative squares in 2 ways.
73348 is the difference of 2 positive pentagonal numbers in 2 ways.
73348 = 1042 + 1262 + 2162 is the sum of 3 positive squares.
733482 is the sum of 3 positive squares.
73348 is a proper divisor of 26334 - 1.
73348 is palindromic in (at least) the following bases: 95, -52, and -74.
73348 in base 51 = SAA and consists of only the digits 'A' and 'S'.

The number 73348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A269652: Number of length-n 0..4 arrays with no adjacent pair x,x+1 repeated.
A269656: T(n,k)=Number of length-n 0..k arrays with no adjacent pair x,x+1 repeated.
A269660: Number of length-7 0..n arrays with no adjacent pair x,x+1 repeated.

Tuesday, February 20, 2018

Number of the day: 99128

Properties of the number 99128:

99128 = 23 × 12391 is the 89611th composite number and is not squarefree.
99128 has 2 distinct prime factors, 8 divisors, 7 antidivisors and 49560 totatives.
99128 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 99128 results in a semiprime.
99128 = 43 + 123 + 463 is the sum of 3 positive cubes in 1 way.
99128 = 247832 - 247812 = 123932 - 123892 is the difference of 2 nonnegative squares in 2 ways.
99128 is the sum of 2 positive triangular numbers.
99128 = 182 + 522 + 3102 is the sum of 3 positive squares.
991282 is the sum of 3 positive squares.
99128 is a proper divisor of 121370 - 1.
99128 in base 26 = 5ggg and consists of only the digits '5' and 'g'.
99128 in base 59 = SS8 and consists of only the digits '8' and 'S'.

The number 99128 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A058493: McKay-Thompson series of class 12e for Monster.
A112149: McKay-Thompson series of class 12f for the Monster group.
A252189: Number of (n+2)X(5+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 1 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 1 3 6 or 7

Monday, February 19, 2018

Number of the day: 6678446

Properties of the number 6678446:

6678446 = 2 × 59 × 56597 is a sphenic number and squarefree.
6678446 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 3282568 totatives.
6678446 has a prime digit sum 41 in base 10.
Reversing the decimal digits of 6678446 results in a sphenic number.
6678446 is the difference of 2 positive pentagonal numbers in 2 ways.
6678446 = 742 + 1792 + 25772 is the sum of 3 positive squares.
66784462 = 33364502 + 57853042 is the sum of 2 positive squares in 1 way.
66784462 is the sum of 3 positive squares.
6678446 is a proper divisor of 106314149 - 1.
6678446 = '6' + '678446' is the concatenation of 2 semiprime numbers.
6678446 = '66' + '78446' is the concatenation of 2 sphenic numbers.