Number of the day: 7266

Properties of the number 7266:

7266 = 2 × 3 × 7 × 173 is the 6337^th composite number and is squarefree.
7266 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 2064 totatives.
7266 has a semiprime digit sum 21 in base 10.
7266 has a Fibonacci digit sum 21 in base 10.
7266 has a triangular digit sum 21 in base 10.
7266 is the sum of 2 positive triangular numbers.
7266 is the difference of 2 positive pentagonal numbers in 3 ways.
7266 is the sum of 3 positive squares.
7266² is the sum of 2 positive squares in 1 way.
7266 is a divisor of 347⁶ - 1.
7266 is palindromic in (at least) base 33.
7266 in base 13 = 33cc and consists of only the digits '3' and 'c'.
7266 in base 33 = 6m6 and consists of only the digits '6' and 'm'.

The number 7266 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A008294: Triangle of coefficients in expansion of D^n (sec x) / sec x in powers of tan x.
A088144: Sum of primitive roots of n-th prime.
A104035: Triangle T(n,k), 0<=k<=n, read by rows, defined by T(0,0) = 1; T(0,k) = 0 if k>0 or if k<0; T(n,k) = k*T(n-1,k-1) + (k+1)*T(n-1,k+1).
A114170: Numbers n such that p(10n) is prime, where p(n) is the number of partitions of n.
A166884: Triangle, read by rows, that transforms diagonals in the table of coefficients of successive iterations of x+x^2+x^3 (cf. A166880).
A185508: Third accumulation array, T, of the natural number array A000027, by antidiagonals.
A200192: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing
A215245: a(n) = minimal value of A215244(k) for 2^n <= k < 2^(n+1).
A241168: Triangle read by rows: T(n,k) (1 <= k <= n) = Steffensen's bracket function [n,n-k].
A255424: Squarefree kernel of A255334: a(n) = A007947(A255334(n)).

Number of the day: 2057

Properties of the number 2057:

2057 = 11² × 17 is the 1746^th composite number and is not squarefree.
2057 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 1760 totatives.
2057 has a semiprime digit sum 14 in base 10.
2057 = 1029² - 1028² = 99² - 88² = 69² - 52² is the difference of 2 nonnegative squares in 3 ways.
2057 is the difference of 2 positive pentagonal numbers in 3 ways.
2057 is the sum of 3 positive squares.
2057 = 11² + 44² is the sum of 2 positive squares in 1 way.
2057² is the sum of 2 positive squares in 1 way.
2057 is a divisor of 727⁴ - 1.
2057 is palindromic in (at least) the following bases: 19, and 26.
2057 in base 7 = 5666 and consists of only the digits '5' and '6'.
2057 in base 15 = 922 and consists of only the digits '2' and '9'.
2057 in base 18 = 665 and consists of only the digits '5' and '6'.
2057 in base 19 = 5d5 and consists of only the digits '5' and 'd'.
2057 in base 25 = 377 and consists of only the digits '3' and '7'.
2057 in base 26 = 313 and consists of only the digits '1' and '3'.

The number 2057 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005902: Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.
A048898: One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-1). Here the 2 (mod 5) numbers (except for n=0).
A051869: 17-gonal (or heptadecagonal) numbers: n(15n-13)/2.
A060354: The n-th n-gonal number.
A074996: Floor of concatenation of n, n+1, n+2, n+3, n+4, n+5 divided by 6.
A083706: 2^(n+1)+n-1.
A140675: a(n) = n*(3*n + 19)/2.
A145812: Odd positive integers a(n) such that for every odd integer m>1 there exists a unique representation of m as a sum of the form a(l)+2a(s)
A160172: T-toothpick sequence (see Comments lines for definition).
A250769: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction

Number of the day: 98596

Properties of the number 98596:

98596 = 2² × 157² is the 89129^th composite number and is not squarefree.
98596 has 2 distinct prime factors, 9 divisors, 6 antidivisors and 48984 totatives.
98596 = 314² is a perfect power of an emirpimes.
98596 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 98596 results in a sphenic number.
98596 = 314² is a perfect square.
98596 = (313 × 314)/2 + (314 × 315)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
98596 = 24650² - 24648² = 314² - 0² is the difference of 2 nonnegative squares in 2 ways.
98596 is the sum of 2 positive triangular numbers.
98596 is the difference of 2 positive pentagonal numbers in 2 ways.
98596 is the sum of 3 positive squares.
98596 = 170² + 264² is the sum of 2 positive squares in 1 way.
98596² is the sum of 2 positive squares in 2 ways.
98596 is a divisor of 233⁷⁸ - 1.
98596 in base 55 = WWa and consists of only the digits 'W' and 'a'.

The number 98596 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A017462: (11*n+6)^2.
A017546: (12n+2)^2.
A028941: Denominator of X-coordinate of n*P where P is generator for rational points on curve y^2+y = x^3-x.
A028945: A006720(n)^2 (squared terms of Somos-4 sequence).
A067178: Smallest square whose sum of digits is A056991(n).
A069262: a(n) = 4*prime(n)^2.
A112735: Exclusionary squares.
A182678: a(n) = the largest n-digit number with exactly 9 divisors, a(n) = 0 if no such number exists.
A192689: Squares for which no final group of decimal digits less than the total forms a square.
A225151: Squares which are a decimal concatenation of triprimes.

Number of the day: 434946

Properties of the number 434946:

434946 = 2 × 3 × 71 × 1021 is the 398385^th composite number and is squarefree.
434946 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 142800 totatives.
434946 has a sphenic digit sum 30 in base 10.
434946 has an oblong digit sum 30 in base 10.
434946 is the sum of 2 positive triangular numbers.
434946 is the difference of 2 positive pentagonal numbers in 2 ways.
434946 is the sum of 3 positive squares.
434946² is the sum of 2 positive squares in 1 way.
434946 is a divisor of 653³⁰ - 1.
434946 = '434' + '946' is the concatenation of 2 sphenic numbers.

Number of the day: 83460358096

Properties of the number 83460358096:

83460358096 = 2⁴ × 31 × 719 × 234029 is composite and not squarefree.
83460358096 has 4 distinct prime factors, 40 divisors, 75 antidivisors and 40327704960 totatives.
83460358096 is the difference of 2 nonnegative squares in 12 ways.
83460358096 is the difference of 2 positive pentagonal numbers in 3 ways.
83460358096 is the sum of 3 positive squares.
83460358096² is the sum of 2 positive squares in 1 way.
83460358096 is a divisor of 89^10245860 - 1.
83460358096 = '8346035809' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 116359

Properties of the number 116359:

116359 is the 10992^th prime.
116359 has 5 antidivisors and 116358 totatives.
116359 has a semiprime digit sum 25 in base 10.
116359 = 58180² - 58179² is the difference of 2 nonnegative squares in 1 way.
116359 is the difference of 2 positive pentagonal numbers in 1 way.
116359 is not the sum of 3 positive squares.
116359 is a divisor of 347²⁴⁶ - 1.
116359 = '11' + '6359' is the concatenation of 2 prime numbers.
116359 is an emirp in (at least) the following bases: 2, 3, 5, 9, 13, 16, 17, 18, 29, 32, 37, 39, 41, 45, 46, 48, 51, 56, 59, 61, 68, 70, 79, 85, 86, 92, and 94.
116359 in base 58 = YYB and consists of only the digits 'B' and 'Y'.
116359 in base 60 = WJJ and consists of only the digits 'J' and 'W'.

The number 116359 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A190758: Primes p such that x^41 = 2 has a solution mod p, and p is congruent to 1 mod 41.

Number of the day: 200444

Properties of the number 200444:

200444 = 2² × 50111 is the 182421^th composite number and is not squarefree.
200444 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 100220 totatives.
200444 has a semiprime digit sum 14 in base 10.
200444 = 50112² - 50110² is the difference of 2 nonnegative squares in 1 way.
200444 is the difference of 2 positive pentagonal numbers in 1 way.
200444 is not the sum of 3 positive squares.
200444 is a divisor of 257⁵⁰¹¹ - 1.

Number of the day: 64825

Properties of the number 64825:

64825 = 5² × 2593 is the 58345^th composite number and is not squarefree.
64825 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 51840 totatives.
64825 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 64825 results in a semiprime.
64825 = 41³ - 16³ is the difference of 2 positive cubes in 1 way.
64825 = 32413² - 32412² = 6485² - 6480² = 1309² - 1284² is the difference of 2 nonnegative squares in 3 ways.
64825 is the sum of 3 positive squares.
64825 = 141² + 212² = 85² + 240² = 76² + 243² is the sum of 2 positive squares in 3 ways.
64825² is the sum of 2 positive squares in 7 ways.
64825 is palindromic in (at least) base 50.
64825 in base 50 = PkP and consists of only the digits 'P' and 'k'.

The number 64825 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A038643: Gaps of 2 in sequence A038593 (lower terms).

Number of the day: 147432654

Properties of the number 147432654:

147432654 = 2 × 3² × 523 × 15661 is composite and not squarefree.
147432654 has 4 distinct prime factors, 24 divisors, 13 antidivisors and 49047120 totatives.
147432654 has a triangular digit sum 36 in base 10.
147432654 is the sum of 3 positive squares.
147432654² is the sum of 2 positive squares in 1 way.

Number of the day: 9377

Properties of the number 9377:

9377 is the 1160^th prime.
9377 has 25 antidivisors and 9376 totatives.
9377 has a semiprime digit sum 26 in base 10.
Reversing the decimal digits of 9377 results in a semiprime.
9377 = 4689² - 4688² is the difference of 2 nonnegative squares in 1 way.
9377 is the sum of 3 positive squares.
9377 = 56² + 79² is the sum of 2 positive squares in 1 way.
9377² is the sum of 2 positive squares in 1 way.
9377 is an emirp in (at least) the following bases: 2, 3, 6, 7, 9, 12, 14, 23, 29, 31, 32, 33, 37, 41, 49, 55, 57, 61, 70, 71, 76, 77, 79, 82, 84, 87, 91, 98, and 100.
9377 in base 12 = 5515 and consists of only the digits '1' and '5'.
9377 in base 23 = hgg and consists of only the digits 'g' and 'h'.
9377 in base 39 = 66H and consists of only the digits '6' and 'H'.
9377 in base 43 = 533 and consists of only the digits '3' and '5'.

The number 9377 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023303: Numbers n such that n remains prime through 4 iterations of function f(x) = 2x + 3.
A059605: a(n)=(1/3!)*(n^3+24*n^2+107*n+90), compare A059604.
A068652: Numbers such that every cyclic permutation is a prime.
A082077: Balanced primes of order two.
A108385: Primes p such that p's set of distinct digits is {3,7,9}.
A142019: Primes congruent to 15 mod 31.
A142125: Primes congruent to 16 mod 37.
A176470: Primes of the form 5*x^2-3*y^2, where x and y are consecutive numbers.
A210498: Prime numbers that become emirps when their least-significant-digit is deleted.
A214675: 9*n^2 - 13*n + 5.

Number of the day: 64185

Properties of the number 64185:

64185 = 3 × 5 × 11 × 389 is the 57756^th composite number and is squarefree.
64185 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 31040 totatives.
64185 = 32093² - 32092² = 10699² - 10696² = 6421² - 6416² = 2923² - 2912² = 2147² - 2132² = 989² - 956² = 611² - 556² = 277² - 112² is the difference of 2 nonnegative squares in 8 ways.
64185 is the sum of 3 positive squares.
64185² is the sum of 2 positive squares in 4 ways.
64185 is palindromic in (at least) the following bases: 44, and 84.
64185 in base 44 = X6X and consists of only the digits '6' and 'X'.
64185 in base 45 = VVF and consists of only the digits 'F' and 'V'.
64185 in base 46 = UFF and consists of only the digits 'F' and 'U'.

The number 64185 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A175773: Expansion of 1/(1 - x - x^6 - x^11 + x^12).
A231675: a(n) = Sum_{i=0..n} digsum_6(i)^4, where digsum_6(i) = A053827(i).

Number of the day: 565852355

Properties of the number 565852355:

565852355 = 5 × 313 × 547 × 661 is composite and squarefree.
565852355 has 4 distinct prime factors, 16 divisors, 17 antidivisors and 449729280 totatives.
565852355 = 282926178² - 282926177² = 56585238² - 56585233² = 904074² - 903761² = 517506² - 516959² = 428358² - 427697² = 181566² - 180001² = 104814² - 102079² = 87258² - 83953² is the difference of 2 nonnegative squares in 8 ways.
565852355 is the sum of 3 positive squares.
565852355² is the sum of 2 positive squares in 13 ways.

Number of the day: 834657

Properties of the number 834657:

834657 = 3 × 278219 is semiprime.
834657 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 556436 totatives.
834657 has a semiprime digit sum 33 in base 10.
834657 = 417329² - 417328² = 139111² - 139108² is the difference of 2 nonnegative squares in 2 ways.
834657 is the sum of 3 positive squares.
834657 is an emirpimes in (at least) the following bases: 9, 18, 21, 25, 27, 36, 39, 41, 42, 57, 59, 67, 82, 84, 85, 91, and 100.

The number 834657 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A254008: Numbers that divide the sum of the reverse of their divisors (A069192).

Number of the day: 992471802

Properties of the number 992471802:

992471802 = 2 × 3 × 7 × 19 × 229 × 5431 is composite.
992471802 has 6 distinct prime factors, 64 divisors, 45 antidivisors and 267416640 totatives.
992471802 has an oblong digit sum 42 in base 10.
992471802 is the sum of 3 positive squares.
992471802² is the sum of 2 positive squares in 1 way.

Number of the day: 572984137611

Properties of the number 572984137611:

572984137611 = 3² × 64483 × 987313 is composite.
572984137611 has 3 distinct prime factors, 12 divisors, 43 antidivisors and 381983114304 totatives.
572984137611 = 286492068806² - 286492068805² = 95497356270² - 95497356267² = 31832452094² - 31832452085² = 4475150² - 4410667² = 1577694² - 1384245² = 783830² - 203483² is the difference of 2 nonnegative squares in 6 ways.
572984137611 is the sum of 3 positive squares.
572984137611² is the sum of 2 positive squares in 1 way.

Number of the day: 3479346

Properties of the number 3479346:

3479346 = 2 × 3² × 13 × 14869 is composite.
3479346 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 1070496 totatives.
3479346 has a triangular digit sum 36 in base 10.
3479346 is the sum of 3 positive squares.
3479346 is the sum of 2 positive squares in 2 ways.
3479346² is the sum of 2 positive squares in 4 ways.

Number of the day: 670878

Properties of the number 670878:

670878 = 2 × 3² × 13 × 47 × 61 is composite.
670878 has 5 distinct prime factors, 48 divisors and 29 antidivisors.
670878 has a triangular digit sum 36 in base 10.
670878 is the sum of 3 positive squares.
670878² is the sum of 2 positive squares in 4 ways.

Number of the day: 31416

In honor of Pi Day 2016 (3.14.16), today's number of the day is 31416 ( = 10000π rounded to an integer).

Properties of the number 31416:

31416 = 2³ × 3 × 7 × 11 × 17 is composite.
31416 has 5 distinct prime factors, 64 divisors and 19 antidivisors.
31416 has a semiprime digit sum 15 in base 10.
31416 has a triangular digit sum 15 in base 10.
31416 has an oblong digit product 72 in base 10.
31416 is the difference of 2 nonnegative squares in 16 ways.
31416 is the sum of 3 positive squares.
31416² is the sum of 2 positive squares in 1 way.
31416 is palindromic in (at least) the following bases: 36, and 57.
31416 in base 33 = ss0 and consists of only the digits '0' and 's'.
31416 in base 36 = o8o and consists of only the digits '8' and 'o'.
31416 in base 38 = LSS and consists of only the digits 'L' and 'S'.
31416 in base 57 = 9c9 and consists of only the digits '9' and 'c'.

The number 31416 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A011546: Decimal expansion of Pi rounded to n places.
A034323: a(n) = n-th quintic factorial number divided by 2.
A050780: (n + sopf_n = m) and (m - sopf_m = n). Sequence gives values of n.
A051799: Partial sums of A007587.
A067048: a(n) = lcm(n, n+1, n+2, n+3, n+4) / 60.
A181337: Number of even entries in the top rows of all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
A189984: Numbers with prime factorization pqrst^3.
A198438: Common differences in triples of squares in arithmetic progression, that are not a multiples of other triples in (A198384,A198385,A198386).
A212514: Number of (w,x,y,z) with all terms in {1,...,n} and w<=2x and y>3z.
A221590: T(n,k)=Equals one maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly one of their king-move neighbors in a random 0..3 nXk array

Bonus number of the day: 663168191

Properties of the number 663168191:

663168191 = 7 × 19² × 262433 is composite.
663168191 has 3 distinct prime factors, 12 divisors and 23 antidivisors.
663168191 has a prime digit sum 41 in base 10.
663168191 = 331584096² - 331584095² = 47369160² - 47369153² = 17451804² - 17451785² = 2493180² - 2493047² = 918696² - 918335² = 132480² - 129953² is the difference of 2 nonnegative squares in 6 ways.
663168191 is not the sum of 3 positive squares.
663168191² is the sum of 2 positive squares in 1 way.

Number of the day: 7276877

Properties of the number 7276877:

7276877 and 7276879 form a twin prime pair.
7276877 has 9 antidivisors.
7276877 is an emirp in (at least) the following bases: 4, 8, 11, 19, 25, 34, 35, 38, 44, 55, 59, 61, 71, 72, and 74.
7276877 = 3638439² - 3638438² is the difference of 2 nonnegative squares in 1 way.
7276877 is the sum of 3 positive squares.
7276877 is the sum of 2 positive squares in 1 way.
7276877² is the sum of 2 positive squares in 1 way.

Number of the day: 6529

Properties of the number 6529:

6529 is prime.
6529 has 7 antidivisors.
6529 is an emirp in (at least) the following bases: 8, 13, 15, 22, 23, 30, 31, 36, 41, 44, 46, 49, 51, 60, 62, 63, 66, 71, 72, 73, 81, 82, 83, 86, 94, and 99.
6529 is palindromic in (at least) the following bases: 64, and 68.
6529 = 3265² - 3264² is the difference of 2 nonnegative squares in 1 way.
6529 is the sum of 3 positive squares.
6529 = 48² + 65² is the sum of 2 positive squares in 1 way.
6529² is the sum of 2 positive squares in 1 way.
6529 in base 3 = 22221211 and consists of only the digits '1' and '2'.
6529 in base 30 = 77j and consists of only the digits '7' and 'j'.
6529 in base 46 = 33h and consists of only the digits '3' and 'h'.

The number 6529 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031936: Lower prime of a difference of 18 between consecutive primes.
A056211: Primes p for which the period of reciprocal = (p-1)/6.
A066540: The first of two consecutive primes with equal digital sums.
A080076: Proth primes: primes of the form k*2^m + 1 with odd k < 2^m, m >= 1.
A111641: Expansion of -(1+x+3*x^2+x^3)/((x^2+4*x+1)*(x^2-2*x-1)).
A142925: Primes congruent to 1 mod 64.
A145048: Primes p of the form 4k+1 for which s=13 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a full square
A154616: Primes of the form (4*n^2-8*n-9)/3.
A208177: Primes of the form 128n + 1.
A233062: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..k+1} nondecreasing, and column sums sum{i*x(i,j), i=1..n+1} nondecreasing

Number of the day: 487

Properties of the number 487:

487 is prime.
487 has 13 antidivisors.
487 has prime digit sum 19 in base 10.
487 is an emirp in (at least) the following bases: 2, 4, 11, 15, 16, 19, 22, 23, 29, 32, 33, 41, 42, 43, 47, 52, 55, 64, 65, 66, 67, 69, 71, 73, 77, 79, 83, 91, 96, 97, and 99.
487 is palindromic in (at least) the following bases: 8, and 18.
487 = 244² - 243² is the difference of 2 nonnegative squares in 1 way.
487 is not the sum of 3 positive squares.
487 in base 8 = 747 and consists of only the digits '4' and '7'.
487 in base 15 = 227 and consists of only the digits '2' and '7'.
487 in base 17 = 1bb and consists of only the digits '1' and 'b'.
487 in base 18 = 191 and consists of only the digits '1' and '9'.

The number 487 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.
A002145: Primes of the form 4n+3.
A002476: Primes of form 6m + 1.
A104272: Ramanujan primes R_n: a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x.
A023200: Primes p such that p + 4 is also prime.
A107132: Primes of the form 2x^2+13y^2.
A007510: Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.
A007645: Generalized cuban primes: primes of the form x^2 + xy + y^2; or primes of the form x^2 + 3*y^2; or primes == 0 or 1 mod 3.
A065727: Primes p such that the decimal expansion of its base 9 conversion is also prime.
A140633: Primes of the form 7x^2+4xy+52y^2.