Number of the day: 629046

Properties of the number 629046:

629046 = 2 × 3⁴ × 11 × 353 is the 577774^th composite number and is not squarefree.
629046 has 4 distinct prime factors, 40 divisors, 23 antidivisors and 190080 totatives.
629046 = 1² + 14² + 793² is the sum of 3 positive squares.
629046² = 400950² + 484704² is the sum of 2 positive squares in 1 way.
629046² is the sum of 3 positive squares.
629046 is a proper divisor of 647¹⁶⁰ - 1.
629046 = '62' + '9046' is the concatenation of 2 semiprime numbers.

Number of the day: 202917

Properties of the number 202917:

202917 = 3 × 11² × 13 × 43 is the 184699^th composite number and is not squarefree.
202917 has 4 distinct prime factors, 24 divisors, 31 antidivisors and 110880 totatives.
202917 has a semiprime digit sum 21 in base 10.
202917 has a Fibonacci digit sum 21 in base 10.
202917 has a triangular digit sum 21 in base 10.
202917 is the difference of 2 nonnegative squares in 12 ways.
202917 is the sum of 2 positive triangular numbers.
202917 is the difference of 2 positive pentagonal numbers in 5 ways.
202917 = 2² + 47² + 448² is the sum of 3 positive squares.
202917² = 78045² + 187308² is the sum of 2 positive squares in 1 way.
202917² is the sum of 3 positive squares.
202917 is a proper divisor of 727¹⁴ - 1.
202917 = '2029' + '17' is the concatenation of 2 prime numbers.
202917 = '202' + '917' is the concatenation of 2 semiprime numbers.
202917 is palindromic in (at least) the following bases: -60, and -62.
202917 in base 32 = 6655 and consists of only the digits '5' and '6'.
202917 in base 34 = 55i5 and consists of only the digits '5' and 'i'.

The number 202917 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A218266: Number of standard Young tableaux of n cells and height >= 6.

Number of the day: 7793

Properties of the number 7793:

7793 is a cyclic number.
7793 is the 987^th prime.
7793 has 13 antidivisors and 7792 totatives.
7793 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7793 results in a semiprime.
7793 = 3897² - 3896² is the difference of 2 nonnegative squares in 1 way.
7793 is the difference of 2 positive pentagonal numbers in 1 way.
7793 = 7² + 88² is the sum of 2 positive squares in 1 way.
7793 = 6² + 19² + 86² is the sum of 3 positive squares.
7793² = 1232² + 7695² is the sum of 2 positive squares in 1 way.
7793² is the sum of 3 positive squares.
7793 is a proper divisor of 43⁴⁸⁷ - 1.
7793 = '77' + '93' is the concatenation of 2 semiprime numbers.
7793 is an emirp in (at least) the following bases: 3, 4, 5, 11, 16, 20, 21, 23, 24, 27, 31, 41, 49, 55, 59, 61, 63, 64, 67, 70, 80, 83, 84, 85, 86, 95, 98, and 100.
7793 is palindromic in (at least) the following bases: 28, 53, -34, and -44.
7793 in base 28 = 9q9 and consists of only the digits '9' and 'q'.
7793 in base 33 = 755 and consists of only the digits '5' and '7'.
7793 in base 52 = 2jj and consists of only the digits '2' and 'j'.
7793 in base 53 = 2f2 and consists of only the digits '2' and 'f'.

The number 7793 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001134: Primes p such that the multiplicative order of 2 modulo p is (p-1)/4.
A051026: Number of primitive subsequences of {1, 2, ..., n}.
A057622: Initial prime in first sequence of n consecutive primes congruent to 5 modulo 6.
A068652: Numbers such that every cyclic permutation is a prime.
A128337: Numbers k such that (7^k + 5^k)/12 is prime.
A142200: Primes congruent to 3 mod 41.
A154577: Primes of the form 2n^2+14n+5.
A293663: Circular primes that are not repunits.
A316652: Number of series-reduced rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n.
A317716: Square array A(n, k), read by antidiagonals downwards: k-th prime p such that cyclic digit shifts produce exactly n different primes.

Number of the day: 75335

Ernst Friedrich Ferdinand Zermelo was born on this day 151 years ago.

Properties of the number 75335:

75335 = 5 × 13 × 19 × 61 is the 67912^th composite number and is squarefree.
75335 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 51840 totatives.
75335 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 75335 results in a semiprime.
75335 = 37668² - 37667² = 7536² - 7531² = 2904² - 2891² = 1992² - 1973² = 648² - 587² = 612² - 547² = 444² - 349² = 276² - 29² is the difference of 2 nonnegative squares in 8 ways.
75335 is the difference of 2 positive pentagonal numbers in 7 ways.
75335 is not the sum of 3 positive squares.
75335² = 45201² + 60268² = 33592² + 67431² = 51129² + 55328² = 18544² + 73017² = 5073² + 75164² = 31407² + 68476² = 38247² + 64904² = 25916² + 70737² = 49324² + 56943² = 28975² + 69540² = 15960² + 73625² = 41040² + 63175² = 13585² + 74100² is the sum of 2 positive squares in 13 ways.
75335² is the sum of 3 positive squares.
75335 is a proper divisor of 1559¹⁰ - 1.
75335 = '753' + '35' is the concatenation of 2 semiprime numbers.
75335 is palindromic in (at least) base 70.
75335 in base 58 = MMp and consists of only the digits 'M' and 'p'.

The number 75335 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A132124: a(n) = n*(n+1)*(8*n + 1)/6.
A137080: Numbers k such that k and k^2 use only the digits 2, 3, 5, 6 and 7.
A345705: Numbers k such that (3^ord(3/2, k) - 2^ord(3/2, k))/k is a prime, where ord(3/2, k) is the multiplicative order of 3/2 (mod k).

Number of the day: 3430

Properties of the number 3430:

3430 = 2 × 5 × 7³ is the 2949^th composite number and is not squarefree.
3430 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 1176 totatives.
3430 has a semiprime digit sum 10 in base 10.
3430 has a triangular digit sum 10 in base 10.
3430 = 7³ + 7³ + 14³ is the sum of 3 positive cubes in 1 way.
3430 is the sum of 2 positive triangular numbers.
3430 is the difference of 2 positive pentagonal numbers in 4 ways.
3430 = 9² + 10² + 57² is the sum of 3 positive squares.
3430² = 2058² + 2744² is the sum of 2 positive squares in 1 way.
3430² is the sum of 3 positive squares.
3430 is a proper divisor of 1373⁴ - 1.
3430 is palindromic in (at least) the following bases: 18, 21, 25, 69, 97, and -19.
3430 in base 16 = d66 and consists of only the digits '6' and 'd'.
3430 in base 18 = aaa and consists of only the digit 'a'.
3430 in base 19 = 99a and consists of only the digits '9' and 'a'.
3430 in base 21 = 7g7 and consists of only the digits '7' and 'g'.
3430 in base 24 = 5mm and consists of only the digits '5' and 'm'.
3430 in base 25 = 5c5 and consists of only the digits '5' and 'c'.
3430 in base 58 = 118 and consists of only the digits '1' and '8'.

The number 3430 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007727: Number of 2n-bead black-white strings with n black beads and fundamental period 2n.
A025632: Numbers of form 7^i*10^j, with i, j >= 0.
A027466: Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j).
A027474: a(n) = 7^(n-2) * C(n,2).
A051682: 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2.
A088409: a(n) = A063416(n)/7.
A208688: T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically
A241638: Number of partitions p of n such that (number of even numbers in p) = (number of odd numbers in p).
A325793: Positive integers whose number of divisors is equal to their sum of prime indices.
A351255: Numbers whose k-th arithmetic derivative is zero for some k>0, ordered by their position in A276086.

Number of the day: 545083

Properties of the number 545083:

545083 is a cyclic number.
545083 = 7 × 11 × 7079 is a sphenic number and squarefree.
545083 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 424680 totatives.
545083 has a semiprime digit sum 25 in base 10.
545083 = 272542² - 272541² = 38938² - 38931² = 24782² - 24771² = 3578² - 3501² is the difference of 2 nonnegative squares in 4 ways.
545083 is the sum of 2 positive triangular numbers.
545083 is the difference of 2 positive pentagonal numbers in 4 ways.
545083 = 85² + 123² + 723² is the sum of 3 positive squares.
545083² is the sum of 3 positive squares.
545083 is a proper divisor of 43⁷⁰⁷⁸ - 1.
545083 = '5' + '45083' is the concatenation of 2 prime numbers.

The number 545083 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A174728: Triangle read by rows: T(n, m, q) = (1-q^n)*Eulerian(n+1, m) - (1-q^n) + 1, with q = 2.

Number of the day: 165801

Charles Émile Picard was born on this day 166 years ago.

Properties of the number 165801:

165801 is a cyclic number.
165801 = 3 × 17 × 3251 is a sphenic number and squarefree.
165801 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 104000 totatives.
165801 has a semiprime digit sum 21 in base 10.
165801 has a Fibonacci digit sum 21 in base 10.
165801 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 165801 results in a semiprime.
165801 = 82901² - 82900² = 27635² - 27632² = 4885² - 4868² = 1651² - 1600² is the difference of 2 nonnegative squares in 4 ways.
165801 is the difference of 2 positive pentagonal numbers in 2 ways.
165801 = 5² + 76² + 400² is the sum of 3 positive squares.
165801² = 78024² + 146295² is the sum of 2 positive squares in 1 way.
165801² is the sum of 3 positive squares.
165801 is a proper divisor of 1237²⁰ - 1.
165801 is palindromic in (at least) the following bases: 50, -64, and -90.
165801 in base 50 = 1GG1 and consists of only the digits '1' and 'G'.

The number 165801 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A005904: Centered dodecahedral numbers.

Number of the day: 7222022

Happy Casual π Day!

Properties of the number 7222022:

7222022 = 2 × 43 × 79 × 1063 is the 6731307^th composite number and is squarefree.
7222022 has 4 distinct prime factors, 16 divisors, 27 antidivisors and 3479112 totatives.
7222022 has an emirp digit sum 17 in base 10.
7222022 = 17² + 42² + 2687² is the sum of 3 positive squares.
7222022² is the sum of 3 positive squares.
7222022 is a proper divisor of 7²³⁴ - 1.

Number of the day: 763856

Properties of the number 763856:

763856 = 2⁴ × 47741 is the 702587^th composite number and is not squarefree.
763856 has 2 distinct prime factors, 10 divisors, 9 antidivisors and 381920 totatives.
763856 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 763856 results in a prime.
763856 = 190965² - 190963² = 95484² - 95480² = 47745² - 47737² is the difference of 2 nonnegative squares in 3 ways.
763856 is the difference of 2 positive pentagonal numbers in 1 way.
763856 = 616² + 620² is the sum of 2 positive squares in 1 way.
763856 = 56² + 204² + 848² is the sum of 3 positive squares.
763856² = 4944² + 763840² is the sum of 2 positive squares in 1 way.
763856² is the sum of 3 positive squares.
763856 is a proper divisor of 1163¹⁴⁰ - 1.
763856 = '76385' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 258031

Properties of the number 258031:

258031 is a cyclic number.
258031 is the 22678^th prime.
258031 has 17 antidivisors and 258030 totatives.
258031 has a prime digit sum 19 in base 10.
258031 = 129016² - 129015² is the difference of 2 nonnegative squares in 1 way.
258031 is the difference of 2 positive pentagonal numbers in 1 way.
258031 is not the sum of 3 positive squares.
258031² is the sum of 3 positive squares.
258031 is a proper divisor of 919¹⁴¹ - 1.
258031 = '2' + '58031' is the concatenation of 2 prime numbers.
258031 = '25' + '8031' is the concatenation of 2 semiprime numbers.
258031 is an emirp in (at least) the following bases: 2, 9, 16, 19, 21, 22, 27, 28, 29, 31, 33, 45, 47, 52, 56, 60, 61, 63, 65, 66, 72, 74, 77, 79, 90, 91, 94, and 95.
258031 is palindromic in (at least) the following bases: 4, and -73.
258031 in base 4 = 332333233 and consists of only the digits '2' and '3'.

The number 258031 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A224605: Number of (n+2) X 9 0..2 matrices with each 3 X 3 subblock idempotent.
A254905: Number of (n+2)X(6+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the diagonal and antidiagonal minus the two minimums of the central column and central row nondecreasing horizontally, vertically and ne-to-sw antidiagonally
A254907: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the diagonal and antidiagonal minus the two minimums of the central column and central row nondecreasing horizontally, vertically and ne-to-sw antidiagonally
A254908: Number of (2+2)X(n+2) 0..1 arrays with every 3X3 subblock sum of the two sums of the diagonal and antidiagonal minus the two minimums of the central column and central row nondecreasing horizontally, vertically and ne-to-sw antidiagonally

Number of the day: 23823322

Properties of the number 23823322:

23823322 = 2 × 1123 × 10607 is a sphenic number and squarefree.
23823322 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 11899932 totatives.
23823322 has a semiprime digit sum 25 in base 10.
23823322 is the difference of 2 positive pentagonal numbers in 3 ways.
23823322 = 24² + 239² + 4875² is the sum of 3 positive squares.
23823322² is the sum of 3 positive squares.
23823322 is a proper divisor of 857⁵⁸³³³ - 1.
23823322 = '238233' + '22' is the concatenation of 2 semiprime numbers.
23823322 = '2382' + '3322' is the concatenation of 2 sphenic numbers.

Number of the day: 72737033

Properties of the number 72737033:

72737033 is a cyclic number.
72737033 = 17 × 4278649 is semiprime and squarefree.
72737033 has 2 distinct prime factors, 4 divisors, 37 antidivisors and 68458368 totatives.
Reversing the decimal digits of 72737033 results in an emirpimes.
72737033 = 36368517² - 36368516² = 2139333² - 2139316² is the difference of 2 nonnegative squares in 2 ways.
72737033 is the difference of 2 positive pentagonal numbers in 2 ways.
72737033 = 2248² + 8227² = 1888² + 8317² is the sum of 2 positive squares in 2 ways.
72737033 = 26² + 209² + 8526² is the sum of 3 positive squares.
72737033² = 36988592² + 62630025² = 34229192² + 64179735² = 31404992² + 65607945² = 3164040² + 72668183² is the sum of 2 positive squares in 4 ways.
72737033² is the sum of 3 positive squares.
72737033 is a proper divisor of 1931¹³⁶⁴⁸ - 1.
72737033 = '7273' + '7033' is the concatenation of 2 semiprime numbers.
72737033 is an emirpimes in (at least) the following bases: 6, 7, 10, 11, 14, 17, 20, 22, 27, 31, 33, 36, 37, 45, 47, 48, 49, 55, 56, 63, 68, 70, 75, 78, 82, 83, 84, 87, 89, 90, 95, 97, and 99.

Number of the day: 7172022

Happy Yellow Pig Day!

Properties of the number 7172022:

7172022 = 2 × 3 × 11 × 13² × 643 is the 6684450^th composite number and is not squarefree.
7172022 has 5 distinct prime factors, 48 divisors, 27 antidivisors and 2003040 totatives.
7172022 has a semiprime digit sum 21 in base 10.
7172022 has a Fibonacci digit sum 21 in base 10.
7172022 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 7172022 results in a sphenic number.
7172022 is the sum of 2 positive triangular numbers.
7172022 is the difference of 2 positive pentagonal numbers in 7 ways.
7172022 = 43² + 62² + 2677² is the sum of 3 positive squares.
7172022² = 2758470² + 6620328² = 5050122² + 5092560² is the sum of 2 positive squares in 2 ways.
7172022² is the sum of 3 positive squares.
7172022 is a proper divisor of 1109³⁹⁰ - 1.
7172022 in base 3 = 111111101011110 and consists of only the digits '0' and '1'.

Number of the day: 250162601912

Properties of the number 250162601912:

250162601912 = 2³ × 31 × 97 × 10399177 is composite and not squarefree.
250162601912 has 4 distinct prime factors, 32 divisors, 31 antidivisors and 119798507520 totatives.
250162601912 has a semiprime digit sum 35 in base 10.
250162601912 = 684³ + 2936³ + 6078³ = 3806³ + 4240³ + 4916³ is the sum of 3 positive cubes in 2 ways.
250162601912 = 62540650479² - 62540650477² = 31270325241² - 31270325237² = 2017440369² - 2017440307² = 1008720231² - 1008720107² = 644749071² - 644748877² = 322374681² - 322374293² = 20801361² - 20795347² = 10405191² - 10393163² is the difference of 2 nonnegative squares in 8 ways.
250162601912 = 466² + 3516² + 500150² is the sum of 3 positive squares.
250162601912² = 168618791040² + 184794563512² = 167634733240² + 185687704512² = 148905717688² + 201018443520² = 24175125312² + 248991748280² is the sum of 2 positive squares in 4 ways.
250162601912² is the sum of 3 positive squares.
250162601912 is a proper divisor of 1297⁸⁶⁶⁵⁹⁸ - 1.

Number of the day: 180293

Properties of the number 180293:

180293 is a cyclic number.
180293 = 29 × 6217 is semiprime and squarefree.
180293 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 174048 totatives.
180293 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 180293 results in an emirpimes.
180293 = 90147² - 90146² = 3123² - 3094² is the difference of 2 nonnegative squares in 2 ways.
180293 is the difference of 2 positive pentagonal numbers in 2 ways.
180293 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
180293 = 257² + 338² = 47² + 422² is the sum of 2 positive squares in 2 ways.
180293 = 40² + 63² + 418² is the sum of 3 positive squares.
180293² = 124340² + 130557² = 48195² + 173732² = 39668² + 175875² = 92568² + 154715² is the sum of 2 positive squares in 4 ways.
180293² is the sum of 3 positive squares.
180293 is a proper divisor of 1151¹⁴ - 1.
180293 is an emirpimes in (at least) the following bases: 4, 5, 7, 8, 9, 10, 13, 15, 21, 23, 24, 26, 29, 31, 34, 35, 36, 40, 42, 44, 45, 48, 49, 50, 51, 52, 55, 57, 59, 69, 75, 77, 82, 83, 92, 95, and 97.
180293 is palindromic in (at least) the following bases: -90, and -91.

The number 180293 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A146422: Number of n X n binary arrays symmetric under horizontal reflection with all ones connected only in a 1010-1111 pattern in any orientation.

Number of the day: 90251429

Properties of the number 90251429:

90251429 is a cyclic number.
90251429 = 89 × 1014061 is semiprime and squarefree.
90251429 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 89237280 totatives.
Reversing the decimal digits of 90251429 results in a prime.
90251429 = 45125715² - 45125714² = 507075² - 506986² is the difference of 2 nonnegative squares in 2 ways.
90251429 is the difference of 2 positive pentagonal numbers in 2 ways.
90251429 = 5390² + 7823² = 4670² + 8273² is the sum of 2 positive squares in 2 ways.
90251429 = 23² + 30² + 9500² is the sum of 3 positive squares.
90251429² = 46633629² + 77269820² = 39548379² + 81124880² = 32147229² + 84331940² = 8058060² + 89890979² is the sum of 2 positive squares in 4 ways.
90251429² is the sum of 3 positive squares.
90251429 is a proper divisor of 1301⁶⁷⁶⁰⁴ - 1.
90251429 is an emirpimes in (at least) the following bases: 11, 15, 17, 25, 26, 33, 34, 35, 38, 41, 42, 45, 47, 49, 57, 58, 70, 71, 73, 74, 75, 79, 82, 84, 85, 87, 88, 90, 94, 95, and 98.