Number of the day: 955738977518

Properties of the number 955738977518:

955738977518 = 2 × 13² × 17 × 2671 × 62273 is composite and not squarefree.
955738977518 has 5 distinct prime factors, 48 divisors, 55 antidivisors and 415000535040 totatives.
955738977518 has a semiprime digit sum 74 in base 10.
Reversing the decimal digits of 955738977518 results in a semiprime.
955738977518 is the difference of 2 positive pentagonal numbers in 11 ways.
955738977518 = 387² + 2782² + 977615² is the sum of 3 positive squares.
955738977518² = 449759518832² + 843299097810² = 142785628882² + 945012834480² = 407884136400² + 864330680018² = 495268593768² + 817401989950² = 90816825918² + 951414366760² = 640965190632² + 708943310530² = 605445506120² + 739508439618² = 44073556670² + 954722218632² = 231664355832² + 927237089090² = 318989671918² + 900934283040² = 282097686368² + 913158194670² = 564036993120² + 771556390382² = 326517570240² + 898233415918² = 274446451950² + 915486831232² = 570473670418² + 766809483840² = 367591914430² + 882220594632² = 231937139720² + 927168893118² = 488169476418² + 821661460360² = 570699241710² + 766641616832² = 672975966418² + 678631226640² = 134594339632² + 946214223570² = 142507599150² + 945054801232² is the sum of 2 positive squares in 22 ways.
955738977518² is the sum of 3 positive squares.
955738977518 is a proper divisor of 257¹⁹⁴³⁷⁶ - 1.
955738977518 = '955' + '738977518' is the concatenation of 2 semiprime numbers.

Number of the day: 976985

Properties of the number 976985:

976985 = 5 × 37 × 5281 is a sphenic number and squarefree.
976985 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 760320 totatives.
Reversing the decimal digits of 976985 results in a semiprime.
976985 = 488493² - 488492² = 97701² - 97696² = 13221² - 13184² = 2733² - 2548² is the difference of 2 nonnegative squares in 4 ways.
976985 is the difference of 2 positive pentagonal numbers in 4 ways.
976985 = 616² + 773² = 332² + 931² = 293² + 944² = 29² + 988² is the sum of 2 positive squares in 4 ways.
976985 = 42² + 55² + 986² is the sum of 3 positive squares.
976985² = 631025² + 745860² = 355015² + 910200² = 40625² + 976140² = 553184² + 805287² = 262108² + 941169² = 57304² + 975303² = 618184² + 756537² = 515151² + 830132² = 218073² + 952336² = 586191² + 781588² = 549224² + 807993² = 301017² + 929456² = 316860² + 924175² is the sum of 2 positive squares in 13 ways.
976985² is the sum of 3 positive squares.
976985 is a proper divisor of 1153¹² - 1.

Number of the day: 829888

Properties of the number 829888:

829888 = 2⁶ × 12967 is the 763731^th composite number and is not squarefree.
829888 has 2 distinct prime factors, 14 divisors, 25 antidivisors and 414912 totatives.
829888 has a prime digit sum 43 in base 10.
829888 = 207473² - 207471² = 103738² - 103734² = 51872² - 51864² = 25942² - 25926² = 12983² - 12951² is the difference of 2 nonnegative squares in 5 ways.
829888 is the sum of 2 positive triangular numbers.
829888 is the difference of 2 positive pentagonal numbers in 1 way.
829888 is not the sum of 3 positive squares.
829888² is the sum of 3 positive squares.
829888 is a proper divisor of 193²¹⁶¹ - 1.

Number of the day: 58200

Properties of the number 58200:

58200 = 2³ × 3 × 5² × 97 is the 52305^th composite number and is not squarefree.
58200 has 4 distinct prime factors, 48 divisors, 19 antidivisors and 15360 totatives.
58200 has an emirpimes digit sum 15 in base 10.
58200 has a triangular digit sum 15 in base 10.
58200 is the difference of 2 nonnegative squares in 12 ways.
58200 is the sum of 2 positive triangular numbers.
58200 is the difference of 2 positive pentagonal numbers in 1 way.
58200 = 20² + 34² + 238² is the sum of 3 positive squares.
58200² = 39000² + 43200² = 5280² + 57960² = 11160² + 57120² = 30552² + 49536² = 25344² + 52392² = 34920² + 46560² = 16296² + 55872² is the sum of 2 positive squares in 7 ways.
58200² is the sum of 3 positive squares.
58200 is a proper divisor of 193⁴ - 1.
58200 in base 5 = 3330300 and consists of only the digits '0' and '3'.
58200 in base 22 = 5a5a and consists of only the digits '5' and 'a'.
58200 in base 58 = HHQ and consists of only the digits 'H' and 'Q'.

The number 58200 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015578: Expansion of x/(1-8x-11x^2).
A018211: Alkane (or paraffin) numbers l(10,n).

Number of the day: 5370

Properties of the number 5370:

5370 = 2 × 3 × 5 × 179 is the 4661^th composite number and is squarefree.
5370 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 1424 totatives.
5370 has an emirpimes digit sum 15 in base 10.
5370 has a triangular digit sum 15 in base 10.
5370 is the sum of 2 positive triangular numbers.
5370 is the difference of 2 positive pentagonal numbers in 1 way.
5370 is the difference of 2 positive pentagonal pyramidal numbers in 2 ways.
5370 = (60 × (3 × 60-1))/2 is a pentagonal number.
5370 = 4² + 5² + 73² is the sum of 3 positive squares.
5370² = 3222² + 4296² is the sum of 2 positive squares in 1 way.
5370² is the sum of 3 positive squares.
5370 is a proper divisor of 359² - 1.
5370 is palindromic in (at least) the following bases: 44, 59, -23, -61, and -91.
5370 in base 22 = b22 and consists of only the digits '2' and 'b'.
5370 in base 43 = 2cc and consists of only the digits '2' and 'c'.
5370 in base 44 = 2Y2 and consists of only the digits '2' and 'Y'.
5370 in base 58 = 1YY and consists of only the digits '1' and 'Y'.
5370 in base 59 = 1W1 and consists of only the digits '1' and 'W'.

The number 5370 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002625: Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
A014633: Even pentagonal numbers.
A049452: Pentagonal numbers with even index.
A196485: T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,2,1,4 for x=0,1,2,3,4
A222604: Number of nX1 0..3 arrays with exactly floor(nX1/2) elements equal to at least one king-move neighbor, with new values introduced in row major 0..3 order
A222747: T(n,k)=Number of nXk 0..3 arrays with exactly floor(nXk/2) elements equal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..3 order
A226253: Number of ways of writing n as the sum of 9 triangular numbers.
A232696: E.g.f. A(x) satisfies: A'(x) = A(x/A'(x)) with A(0)=1.
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A263373: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.

Number of the day: 672028146

Properties of the number 672028146:

672028146 = 2 × 3² × 37334897 is the 637149995^th composite number and is not squarefree.
672028146 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 224009376 totatives.
672028146 has a triangular digit sum 36 in base 10.
672028146 is the sum of 2 positive triangular numbers.
672028146 is the difference of 2 positive pentagonal numbers in 2 ways.
672028146 = 4875² + 25461² is the sum of 2 positive squares in 1 way.
672028146 = 929² + 1324² + 25873² is the sum of 3 positive squares.
672028146² = 248244750² + 624496896² is the sum of 2 positive squares in 1 way.
672028146² is the sum of 3 positive squares.
672028146 is a proper divisor of 1789²⁶⁴¹⁶² - 1.
672028146 = '67202' + '8146' is the concatenation of 2 semiprime numbers.

Number of the day: 3930

Gerolamo Cardano was born on this day 516 years ago.

Properties of the number 3930:

3930 = 2 × 3 × 5 × 131 is the 3384^th composite number and is squarefree.
3930 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 1040 totatives.
3930 has an emirpimes digit sum 15 in base 10.
3930 has a triangular digit sum 15 in base 10.
3930 = 26² + … + 30² is the sum of at least 2 consecutive positive squares in 1 way.
3930 is the difference of 2 positive pentagonal numbers in 1 way.
3930 = 7² + 20² + 59² is the sum of 3 positive squares.
3930² = 2358² + 3144² is the sum of 2 positive squares in 1 way.
3930² is the sum of 3 positive squares.
3930 is a proper divisor of 1049² - 1.
3930 is palindromic in (at least) the following bases: 33, and -20.
3930 in base 19 = agg and consists of only the digits 'a' and 'g'.
3930 in base 32 = 3qq and consists of only the digits '3' and 'q'.
3930 in base 33 = 3k3 and consists of only the digits '3' and 'k'.
3930 in base 62 = 11O and consists of only the digits '1' and 'O'.

The number 3930 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A027578: Sums of five consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2.
A075386: Sum of terms of n-th group in A075383.
A076409: Sum of the quadratic residues of prime(n).
A113744: Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, ..., 1, for n>=1.
A138989: a(n) = Frobenius number for 3 successive primes = F[p(n),p(n+1),p(n+2)].
A211978: Total number of parts in all partitions of n plus the sum of largest parts of all partitions of n.
A251829: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 3 or 6 and every diagonal and antidiagonal sum 3 or 6
A256874: Numbers divisible by prime(d) for each digit d in their base 4 representation, none of which may be zero.
A282035: Sum of quadratic residues of (n-th prime == 3 mod 4).
A284949: Triangle read by rows: T(n,k) = number of reversible string structures of length n using exactly k different symbols.