Saturday, April 29, 2017

Number of the day: 841074

Henri Poincaré was born on this day 163 years ago.

Properties of the number 841074:

841074 = 2 × 3 × 13 × 41 × 263 is the 774107th composite number and is squarefree.
841074 has 5 distinct prime factors, 32 divisors, 27 antidivisors and 251520 totatives.
841074 is the sum of 2 positive triangular numbers.
841074 is the difference of 2 positive pentagonal numbers in 2 ways.
841074 = 322 + 2232 + 8892 is the sum of 3 positive squares.
8410742 = 1846262 + 8205602 = 1451762 + 8284502 = 4860242 + 6864302 = 3234902 + 7763762 is the sum of 2 positive squares in 4 ways.
8410742 is the sum of 3 positive squares.
841074 is a divisor of 157960 - 1.
841074 = '84107' + '4' is the concatenation of 2 semiprime numbers.

Friday, April 28, 2017

Number of the day: 74002

Kurt Gödel was born on this day 111 years ago.

Properties of the number 74002:

74002 = 2 × 163 × 227 is a sphenic number and squarefree.
74002 has 3 distinct prime factors, 8 divisors, 53 antidivisors and 36612 totatives.
74002 has an emirp digit sum 13 in base 10.
74002 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 74002 results in a prime.
74002 is the difference of 2 positive pentagonal numbers in 3 ways.
74002 = 32 + 522 + 2672 is the sum of 3 positive squares.
740022 is the sum of 3 positive squares.
74002 is a divisor of 907162 - 1.
74002 is palindromic in (at least) the following bases: 44, 46, 64, and 66.
74002 in base 16 = 12112 and consists of only the digits '1' and '2'.
74002 in base 17 = f111 and consists of only the digits '1' and 'f'.
74002 in base 44 = c9c and consists of only the digits '9' and 'c'.
74002 in base 46 = YiY and consists of only the digits 'Y' and 'i'.

The number 74002 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A032936: Numbers whose set of base 16 digits is {1,2}.

Thursday, April 27, 2017

Number of the day: 74981

Properties of the number 74981:

74981 = 97 × 773 is semiprime and squarefree.
74981 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 74112 totatives.
74981 has a prime digit sum 29 in base 10.
74981 has a triangular digit product 2016 in base 10.
Reversing the decimal digits of 74981 results in a prime.
74981 = 374912 - 374902 = 4352 - 3382 is the difference of 2 nonnegative squares in 2 ways.
74981 is the difference of 2 positive pentagonal numbers in 2 ways.
74981 = 1302 + 2412 = 652 + 2662 is the sum of 2 positive squares in 2 ways.
74981 = 62 + 312 + 2722 is the sum of 3 positive squares.
749812 = 502452 + 556562 = 345802 + 665312 = 411812 + 626602 = 189152 + 725562 is the sum of 2 positive squares in 4 ways.
749812 is the sum of 3 positive squares.
74981 is a divisor of 122948 - 1.
74981 is an emirpimes in (at least) the following bases: 5, 13, 14, 15, 16, 19, 20, 34, 35, 36, 41, 43, 44, 45, 46, 47, 52, 54, 61, 67, 69, 71, 74, 75, 80, 81, 83, 88, 89, 91, 93, 99, and 100.
74981 is palindromic in (at least) the following bases: -20, and -85.
74981 in base 49 = VBB and consists of only the digits 'B' and 'V'.

Wednesday, April 26, 2017

Number of the day: 63348

Properties of the number 63348:

63348 = 22 × 3 × 5279 is the 57000th composite number and is not squarefree.
63348 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 21112 totatives.
63348 has sum of divisors equal to 147840 which is an oblong number.
63348 = 158382 - 158362 = 52822 - 52762 is the difference of 2 nonnegative squares in 2 ways.
63348 is the difference of 2 positive pentagonal numbers in 1 way.
63348 = 202 + 382 + 2482 is the sum of 3 positive squares.
633482 is the sum of 3 positive squares.
63348 is a divisor of 54114 - 1.
63348 is palindromic in (at least) the following bases: 44, and -97.
63348 in base 44 = WVW and consists of only the digits 'V' and 'W'.

The number 63348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A054209: Consider all integer triples (i,j,k), j >= k>0, with i^3=binomial(j+2,3)+binomial(k+2,3), ordered by increasing i; sequence gives j values.
A126411: Number of base 24 n-digit numbers with adjacent digits differing by two or less.

Tuesday, April 25, 2017

Number of the day: 45567089187007

Felix Klein was born on this day 168 years ago.

Andrey Kolmogorov was born on this day 114 years ago.

Properties of the number 45567089187007:

45567089187007 = 292 × 2351 × 3361 × 6857 is composite and not squarefree.
45567089187007 has 4 distinct prime factors, 24 divisors, 117 antidivisors and 43957600512000 totatives.
45567089187007 has a prime digit sum 67 in base 10.
45567089187007 is the difference of 2 nonnegative squares in 12 ways.
45567089187007 is the difference of 2 positive pentagonal numbers in 11 ways.
45567089187007 is not the sum of 3 positive squares.
455670891870072 = 227767657941602 + 394661697778572 = 193266960165752 + 412654630176322 = 260607515277452 + 373790963880322 = 128708361879932 + 437115681805002 = 90946894342682 + 446502658566652 = 165531311392682 + 424541336793352 = 107245280648202 + 442870648695932 = 69071084716552 + 450405536104682 = 144637463449852 + 432106428862682 = 208256484021432 + 405296432948402 = 172919627469682 + 421586010362552 = 242074772073682 + 386051507474252 = 246737172746572 + 383088409225202 = 213154680590322 + 402741907231052 = 278520502202322 + 360641500039352 = 314255787496602 + 329968576871432 = 284959008707452 + 355576046794682 = 301955035948682 + 341261070095752 = 22214633254072 + 455129071546802 = 16695367137682 + 455364937620152 = 60962648570322 + 451574486853452 = 38875232863352 + 454009557132322 is the sum of 2 positive squares in 22 ways.
455670891870072 is the sum of 3 positive squares.
45567089187007 is a divisor of 13711278120 - 1.
45567089187007 = '455' + '67089187007' is the concatenation of 2 sphenic numbers.

Monday, April 24, 2017

Number of the day: 4230

Properties of the number 4230:

4230 = 2 × 32 × 5 × 47 is the 3650th composite number and is not squarefree.
4230 has 4 distinct prime factors, 24 divisors, 13 antidivisors and 1104 totatives.
4230 has a semiprime digit sum 9 in base 10.
4230 = 312 + … + 342 is the sum of at least 2 consecutive positive squares in 1 way.
4230 is the sum of 2 positive triangular numbers.
4230 is the difference of 2 positive pentagonal numbers in 1 way.
4230 = 12 + 22 + 652 is the sum of 3 positive squares.
42302 = 25382 + 33842 is the sum of 2 positive squares in 1 way.
42302 is the sum of 3 positive squares.
4230 is a divisor of 12234 - 1.
4230 = '42' + '30' is the concatenation of 2 sphenic numbers.
4230 = '42' + '30' is the concatenation of 2 oblong numbers.
4230 is palindromic in (at least) the following bases: 17, 20, 21, 89, 93, and -19.
4230 in base 17 = eae and consists of only the digits 'a' and 'e'.
4230 in base 20 = aba and consists of only the digits 'a' and 'b'.
4230 in base 21 = 9c9 and consists of only the digits '9' and 'c'.
4230 in base 26 = 66i and consists of only the digits '6' and 'i'.
4230 in base 32 = 446 and consists of only the digits '4' and '6'.
4230 in base 37 = 33C and consists of only the digits '3' and 'C'.

The number 4230 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000500: Number of permutations of an n-sequence discordant with three given permutations (see reference) in n-7 places.
A027575: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2.
A054000: a(n) = 2*n^2 - 2.
A125014: Numbers n for which nontrivial positive magic squares of exactly 7 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.
A126011: A106486-encodings for the minimal representatives of each equivalence class of the finite combinatorial games.
A135191: Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=6.
A201596: Record (maximal) gaps between prime triplets (p, p+4, p+6).
A210095: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays containing all values 0..2 with every 2X2 subblock having one or two distinct values, and new values 0..2 introduced in row major order
A230899: T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero
A256753: Numbers n such that n is both the average of some twin prime pair p, q (q = p+2) (i.e., n = p+1 = q-1) and is also the average of the prime before p and the prime after q.

Sunday, April 23, 2017

Number of the day: 378766

Properties of the number 378766:

378766 = 2 × 229 × 827 is a sphenic number and squarefree.
378766 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 188328 totatives.
378766 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 378766 results in a semiprime.
378766 is the sum of 2 positive triangular numbers.
378766 is the difference of 2 positive pentagonal numbers in 3 ways.
378766 = 102 + 212 + 6152 is the sum of 3 positive squares.
3787662 = 992402 + 3655342 is the sum of 2 positive squares in 1 way.
3787662 is the sum of 3 positive squares.
378766 is a divisor of 1373118 - 1.
378766 is palindromic in (at least) base 90.