Number of the day: 2477

Carl Ludwig Siegel was born on this day 122 years ago.

Properties of the number 2477:

2477 is a cyclic number.
2477 is the 367^th prime.
2477 has 9 antidivisors and 2476 totatives.
2477 has an oblong digit sum 20 in base 10.
2477 = 4³ + 6³ + 13³ is the sum of 3 positive cubes in 1 way.
2477 = 1239² - 1238² is the difference of 2 nonnegative squares in 1 way.
2477 is the difference of 2 positive pentagonal numbers in 1 way.
2477 = 19² + 46² is the sum of 2 positive squares in 1 way.
2477 = 2² + 13² + 48² is the sum of 3 positive squares.
2477² = 1748² + 1755² is the sum of 2 positive squares in 1 way.
2477² is the sum of 3 positive squares.
2477 is a proper divisor of 19⁶¹⁹ - 1.
2477 is an emirp in (at least) the following bases: 3, 5, 15, 18, 19, 31, 36, 37, 39, 40, 42, 43, 46, 47, 49, 50, 53, 59, 60, 61, 62, 66, 67, 71, 77, 79, 83, 85, 91, 95, 96, 98, and 99.
2477 is palindromic in (at least) the following bases: 33, -14, -19, -24, and -45.
2477 in base 18 = 7bb and consists of only the digits '7' and 'b'.
2477 in base 32 = 2dd and consists of only the digits '2' and 'd'.
2477 in base 33 = 292 and consists of only the digits '2' and '9'.
2477 in base 49 = 11R and consists of only the digits '1' and 'R'.

The number 2477 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000230: Smallest prime p such that there is a gap of 2n between p and next prime.
A038580: Primes with indices that are primes with prime indices.
A049079: Primes prime(k) for which A049076(k) = 3.
A053001: Largest prime < n^2.
A054804: First term of strong prime quartets: prime(m+1)-prime(m) > prime(m+2)-prime(m+1) > prime(m+3)-prime(m+2).
A057190: Numbers n such that (24^n+1)/25 is a prime.
A075580: Smallest prime p(k) such that the number of distinct prime divisors of all composite numbers between p(k) and p(k+1) is n.
A232047: T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors
A272285: Primes of the form 43*n^2 - 537*n + 2971 in order of increasing nonnegative values of n.
A299264: Partial sums of A299258.

Number of the day: 3506

Properties of the number 3506:

3506 = 2 × 1753 is semiprime and squarefree.
3506 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 1752 totatives.
3506 has a semiprime digit sum 14 in base 10.
3506 has sum of divisors equal to 5262 which is a sphenic number.
Reversing the decimal digits of 3506 results in a prime.
3506 = 5² + 59² is the sum of 2 positive squares in 1 way.
3506 = 1² + 16² + 57² is the sum of 3 positive squares.
3506² = 590² + 3456² is the sum of 2 positive squares in 1 way.
3506² is the sum of 3 positive squares.
3506 is a proper divisor of 1571⁶ - 1.
3506 is an emirpimes in (at least) the following bases: 2, 3, 4, 5, 6, 7, 12, 15, 17, 18, 19, 26, 27, 29, 32, 34, 35, 39, 41, 48, 51, 52, 54, 55, 58, 60, 63, 64, 66, 71, 73, 74, 77, 81, 84, 87, 90, 91, 92, 93, 94, 98, and 100.
3506 is palindromic in (at least) the following bases: 31, -5, -19, -22, -25, -34, and -48.
3506 in base 8 = 6662 and consists of only the digits '2' and '6'.
3506 in base 18 = aee and consists of only the digits 'a' and 'e'.
3506 in base 24 = 622 and consists of only the digits '2' and '6'.
3506 in base 29 = 44q and consists of only the digits '4' and 'q'.
3506 in base 30 = 3qq and consists of only the digits '3' and 'q'.
3506 in base 31 = 3k3 and consists of only the digits '3' and 'k'.

The number 3506 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000070: a(n) = Sum_{k=0..n} p(k) where p(k) = number of partitions of k (A000041).
A025065: Number of palindromic partitions of n.
A025414: a(n) is the smallest number that is the sum of 3 nonzero squares in exactly n ways.
A071609: Squared radii of the spheres around (0,0,0) that contain record numbers of lattice points.
A077055: Call two meanders from A005316 equivalent if they differ by a reflection in the Y axis (if n even) or by reflections in the X or Y axes (if n odd). Sequence gives number of inequivalent meanders with n crossings.
A119735: Numbers n such that every digit occurs at least once in n^3.
A120919: Cascadence of (1+x)^3; a triangle, read by rows of 3n+1 terms, that retains its original form upon convolving each row with [1,3,3,1] and then letting excess terms spill over from each row into the initial positions of the next row such that only 3n+1 terms remain in row n for n>=0.
A154493: a(n+1)-+a(n)=prime, a(n+1)*a(n)=Average of twin prime pairs, a(0)=1,a(1)=4.
A224728: T(n,k)=Number of (n+3)X(k+3) 0..2 matrices with each 4X4 subblock idempotent
A281541: Expansion of Sum_{i>=1} x^(i^2)/(1 - x^(i^2)) / Product_{j>=1} (1 - x^(j^2)).

Number of the day: 769169

Properties of the number 769169:

769169 is a cyclic number.
769169 is the 61674^th prime.
769169 has 9 antidivisors and 769168 totatives.
769169 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 769169 results in a semiprime.
769169 = 384585² - 384584² is the difference of 2 nonnegative squares in 1 way.
769169 is the difference of 2 positive pentagonal numbers in 1 way.
769169 = 385² + 788² is the sum of 2 positive squares in 1 way.
769169 = 13² + 110² + 870² is the sum of 3 positive squares.
769169² = 472719² + 606760² is the sum of 2 positive squares in 1 way.
769169² is the sum of 3 positive squares.
769169 is a proper divisor of 101⁴⁸⁰⁷³ - 1.
769169 is an emirp in (at least) the following bases: 7, 11, 13, 14, 17, 18, 26, 27, 28, 29, 34, 45, 46, 55, 61, 71, 78, 79, 85, 87, 89, and 97.

Number of the day: 27243

John von Neumann was born on this day 115 years ago.

Properties of the number 27243:

27243 = 3³ × 1009 is the 24260^th composite number and is not squarefree.
27243 has 2 distinct prime factors, 8 divisors, 17 antidivisors and 18144 totatives.
27243 = 3³ + 6³ + 30³ = 12³ + 18³ + 27³ is the sum of 3 positive cubes in 2 ways.
27243 = 13622² - 13621² = 4542² - 4539² = 1518² - 1509² = 518² - 491² is the difference of 2 nonnegative squares in 4 ways.
27243 is the difference of 2 positive pentagonal numbers in 1 way.
27243 = 7² + 25² + 163² is the sum of 3 positive squares.
27243² = 15093² + 22680² is the sum of 2 positive squares in 1 way.
27243² is the sum of 3 positive squares.
27243 is a proper divisor of 337⁹ - 1.
27243 = '2' + '7243' is the concatenation of 2 prime numbers.
27243 in base 3 = 1101101000 and consists of only the digits '0' and '1'.

The number 27243 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002255: Numbers n such that 7*4^n + 1 is prime.
A009474: a(n) is the concatenation of n and 9n.
A191573: Number of n X n symmetric binary matrices with each 1 adjacent to no more than 5 knight-move neighboring 1s
A225967: Number of permutations of [n] having exactly 6 strong fixed blocks.
A228064: Difference between the number of primes with n digits (A006879) and the nearest integer to F[4n](S(n)), where F[4n](x) are Fibonacci polynomials and S(n) = Sum_{i=0..3} (C(i)*(log(log(A*(B+n^2))))^i) (see A228063).

Number of the day: 980312690405418

Johannes Kepler was born on this day 447 years ago.

Johannes Kepler was born on this day 447 years ago.

Jacob Bernoulli was born on this day 364 years ago.

Properties of the number 980312690405418:

980312690405418 = 2 × 3 × 31 × 53 × 1123 × 4723 × 18749 is composite and squarefree.
980312690405418 has 7 distinct prime factors, 128 divisors, 75 antidivisors and 309904853955840 totatives.
980312690405418 = 59357³ + 71480³ + 74045³ is the sum of 3 positive cubes in 1 way.
980312690405418 is the sum of 2 positive triangular numbers.
980312690405418 is the difference of 2 positive pentagonal numbers in 15 ways.
980312690405418 = 220² + 12637² + 31309943² is the sum of 3 positive squares.
980312690405418² = 517901043987768² + 832340963551770² = 359348774368470² + 912075341915232² = 80571943007568² + 976995973875990² = 584558956676760² + 786958573966182² is the sum of 2 positive squares in 4 ways.
980312690405418² is the sum of 3 positive squares.
980312690405418 is a proper divisor of 433^22958364 - 1.
980312690405418 = '98031' + '2690405418' is the concatenation of 2 sphenic numbers.

Number of the day: 93538

Charles Babbage was born on this day 227 years ago.

Properties of the number 93538:

93538 = 2 × 46769 is semiprime and squarefree.
93538 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 46768 totatives.
93538 has a triangular digit sum 28 in base 10.
93538 has a triangular digit product 3240 in base 10.
Reversing the decimal digits of 93538 results in an emirpimes.
93538 = 6³ + 13³ + 45³ is the sum of 3 positive cubes in 1 way.
93538 is the sum of 2 positive triangular numbers.
93538 is the difference of 2 positive pentagonal numbers in 2 ways.
93538 = 73² + 297² is the sum of 2 positive squares in 1 way.
93538 = 28² + 135² + 273² is the sum of 3 positive squares.
93538² = 43362² + 82880² is the sum of 2 positive squares in 1 way.
93538² is the sum of 3 positive squares.
93538 is a proper divisor of 1213¹⁴⁸ - 1.
93538 = '93' + '538' is the concatenation of 2 emirpimes.
93538 is an emirpimes in (at least) the following bases: 5, 8, 10, 11, 19, 20, 26, 27, 30, 31, 32, 34, 35, 37, 38, 39, 44, 45, 49, 50, 51, 59, 60, 63, 64, 69, 70, 74, 75, 80, 85, 86, 90, 92, 96, 98, and 100.
93538 is palindromic in (at least) the following bases: 61, -16, -50, -78, and -87.
93538 in base 40 = 1III and consists of only the digits '1' and 'I'.
93538 in base 49 = ckk and consists of only the digits 'c' and 'k'.
93538 in base 60 = Pww and consists of only the digits 'P' and 'w'.
93538 in base 61 = P8P and consists of only the digits '8' and 'P'.

The number 93538 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A065455: Number of (binary) bit strings of length n in which no even block of 0's is followed by an odd block of 1's.
A109084: G.f. A(x) satisfies: A(x) = 1/G000041(x/A(x)) where G000041(x) is the g.f. of the partition numbers A000041.
A212830: Number of 0..n arrays of length n+1 with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..n order
A296918: List of coefficients of reduced chromatic polynomial of dodecahedron, highest order terms first.

Number of the day: 48739

Properties of the number 48739:

48739 is a cyclic number.
48739 = 17 × 47 × 61 is a sphenic number and squarefree.
48739 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 44160 totatives.
48739 has an emirp digit sum 31 in base 10.
48739 = 24370² - 24369² = 1442² - 1425² = 542² - 495² = 430² - 369² is the difference of 2 nonnegative squares in 4 ways.
48739 is the difference of 2 positive pentagonal numbers in 4 ways.
48739 = 7² + 27² + 219² is the sum of 3 positive squares.
48739² = 22936² + 43005² = 14805² + 46436² = 30315² + 38164² = 8789² + 47940² is the sum of 2 positive squares in 4 ways.
48739² is the sum of 3 positive squares.
48739 is a proper divisor of 1597⁴ - 1.
48739 = '4873' + '9' is the concatenation of 2 semiprime numbers.

The number 48739 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A185265: a(0)=1, a(1)=2; thereafter a(n) = f(n-1) + f(n-2) where f() = A164387().

Number of the day: 449211

Srinivasa Ramanujan was born on this day 131 years ago.

Properties of the number 449211:

449211 = 3 × 7 × 21391 is a sphenic number and squarefree.
449211 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 256680 totatives.
449211 has a semiprime digit sum 21 in base 10.
449211 has a Fibonacci digit sum 21 in base 10.
449211 has a triangular digit sum 21 in base 10.
449211 = 224606² - 224605² = 74870² - 74867² = 32090² - 32083² = 10706² - 10685² is the difference of 2 nonnegative squares in 4 ways.
449211 is the difference of 2 positive pentagonal numbers in 2 ways.
449211 = 29² + 59² + 667² is the sum of 3 positive squares.
449211² is the sum of 3 positive squares.
449211 is a proper divisor of 241¹³⁸ - 1.
449211 = '449' + '211' is the concatenation of 2 prime numbers.
449211 is palindromic in (at least) base 84.

Number of the day: 2870581

Properties of the number 2870581:

2870581 = 7 × 127 × 3229 is a sphenic number and squarefree.
2870581 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 2440368 totatives.
2870581 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 2870581 results in a semiprime.
2870581 = 1435291² - 1435290² = 205045² - 205038² = 11365² - 11238² = 2059² - 1170² is the difference of 2 nonnegative squares in 4 ways.
2870581 is the sum of 2 positive triangular numbers.
2870581 is the difference of 2 positive pentagonal numbers in 4 ways.
2870581 = 34² + 81² + 1692² is the sum of 3 positive squares.
2870581² = 1574419² + 2400300² is the sum of 2 positive squares in 1 way.
2870581² is the sum of 3 positive squares.
2870581 is a proper divisor of 839⁸⁴ - 1.

Number of the day: 13196

Properties of the number 13196:

13196 = 2² × 3299 is the 11625^th composite number and is not squarefree.
13196 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 6596 totatives.
13196 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 13196 results in a semiprime.
13196 = 3300² - 3298² is the difference of 2 nonnegative squares in 1 way.
13196 is the difference of 2 positive pentagonal numbers in 1 way.
13196 = 14² + 30² + 110² is the sum of 3 positive squares.
13196² is the sum of 3 positive squares.
13196 is a proper divisor of 179³⁴ - 1.
13196 is palindromic in (at least) the following bases: 25, 32, 91, -8, -38, -42, and -79.
13196 in base 3 = 200002202 and consists of only the digits '0' and '2'.
13196 in base 12 = 7778 and consists of only the digits '7' and '8'.
13196 in base 25 = l2l and consists of only the digits '2' and 'l'.
13196 in base 32 = csc and consists of only the digits 'c' and 's'.

The number 13196 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A023621: Convolution of Lucas numbers and A000201.
A024532: a(n) = [ (3rd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, where p(0) = 1.
A055291: Number of trees with n nodes and 4 leaves.
A104909: a(n) = A104908(n) - 10*A104863(n).
A117496: Numbers with no 1's in base 3 & 4 expansions.
A121718: Write 0, 1, ..., n in base 3 and add as if they were decimal numbers.
A224668: Number of 6 X 6 0..n matrices with each 2 X 2 subblock idempotent.
A253503: Number of (n+2) X (1+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.
A258440: Number of squares of all sizes in polyominoes obtained by union of two bi-symmetric figures (A241526) with intersection equals A173196.
A272453: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 478", based on the 5-celled von Neumann neighborhood.

Number of the day: 59868970

Properties of the number 59868970:

59868970 = 2 × 5 × 7 × 855271 is the 56314141^th composite number and is squarefree.
59868970 has 4 distinct prime factors, 16 divisors, 9 antidivisors and 20526480 totatives.
59868970 is the sum of 2 positive triangular numbers.
59868970 is the difference of 2 positive pentagonal numbers in 4 ways.
59868970 = 103² + 300² + 7731² is the sum of 3 positive squares.
59868970² = 35921382² + 47895176² is the sum of 2 positive squares in 1 way.
59868970² is the sum of 3 positive squares.
59868970 is a proper divisor of 491⁴⁵ - 1.

Number of the day: 67866

Marius Sophus Lie was born on this day 176 years ago.

Properties of the number 67866:

67866 = 2 × 3 × 11311 is a sphenic number and squarefree.
67866 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 22620 totatives.
67866 has a semiprime digit sum 33 in base 10.
67866 is the sum of 2 positive triangular numbers.
67866 = 56² + 61² + 247² is the sum of 3 positive squares.
67866² is the sum of 3 positive squares.
67866 is a proper divisor of 967¹³ - 1.
67866 = '678' + '66' is the concatenation of 2 sphenic numbers.
67866 = '6786' + '6' is the concatenation of 2 triangular numbers.
67866 in base 12 = 33336 and consists of only the digits '3' and '6'.

The number 67866 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A104268: a(n) = 2*4^(n-1) - (3n-1)/(2n+2)*C(2n,n).

Number of the day: 4590770284305

Properties of the number 4590770284305:

4590770284305 = 3² × 5 × 43 × 23549 × 100747 is composite and not squarefree.
4590770284305 has 5 distinct prime factors, 48 divisors, 53 antidivisors and 2391345742464 totatives.
4590770284305 is the difference of 2 nonnegative squares in 24 ways.
4590770284305 is the difference of 2 positive pentagonal numbers in 7 ways.
4590770284305 = 280² + 1079² + 2142608² is the sum of 3 positive squares.
4590770284305² = 2754462170583² + 3672616227444² = 2651881877424² + 3747358311057² = 2854937052936² + 3595066929423² = 126909484695² + 4589015775300² is the sum of 2 positive squares in 4 ways.
4590770284305² is the sum of 3 positive squares.
4590770284305 is a proper divisor of 389²³⁵⁰⁷⁴ - 1.
4590770284305 = '45907702' + '84305' is the concatenation of 2 sphenic numbers.

Number of the day: 4948

János Bolyai was born on this day 216 years ago.

Properties of the number 4948:

4948 = 2² × 1237 is the 4286^th composite number and is not squarefree.
4948 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 2472 totatives.
4948 has a semiprime digit sum 25 in base 10.
4948 has sum of divisors equal to 8666 which is a sphenic number.
Reversing the decimal digits of 4948 results in a sphenic number.
4948 = 2³ + 3³ + 17³ is the sum of 3 positive cubes in 1 way.
4948 = 1238² - 1236² is the difference of 2 nonnegative squares in 1 way.
4948 is the sum of 2 positive triangular numbers.
4948 is the difference of 2 positive pentagonal numbers in 1 way.
4948 = 18² + 68² is the sum of 2 positive squares in 1 way.
4948 = 18² + 32² + 60² is the sum of 3 positive squares.
4948² = 2448² + 4300² is the sum of 2 positive squares in 1 way.
4948² is the sum of 3 positive squares.
4948 is a proper divisor of 691⁴ - 1.
4948 is palindromic in (at least) the following bases: 51, -18, -26, -27, -43, and -97.
4948 in base 19 = dd8 and consists of only the digits '8' and 'd'.
4948 in base 26 = 788 and consists of only the digits '7' and '8'.
4948 in base 40 = 33S and consists of only the digits '3' and 'S'.
4948 in base 49 = 22m and consists of only the digits '2' and 'm'.
4948 in base 50 = 1mm and consists of only the digits '1' and 'm'.
4948 in base 51 = 1k1 and consists of only the digits '1' and 'k'.

The number 4948 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A097545: Numerators of "Farey fraction" approximations to Pi.
A101135: a(1)=1. a(n) = a(n-1) + sum of the squares which are among the first (n-1) terms of the sequence.
A138854: Numbers which are the sum of three cubes of distinct primes.
A163937: Triangle related to the o.g.f.s. of the right hand columns of A028421 (E(x,m=2,n)).
A179186: Numbers n such that phi(n) = phi(n+4), with Euler's totient function phi=A000010.
A190402: Number n for which phi(n) = phi(n'), where phi is the Euler totient function and n' the arithmetic derivative of n.
A227025: T(n,k)=Number of nXk (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order
A241638: Number of partitions p of n such that (number of even numbers in p) = (number of odd numbers in p).
A269011: T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
A300120: Number of skew partitions whose quotient diagram is connected and whose numerator has weight n.

Number of the day: 94440

Properties of the number 94440:

94440 = 2³ × 3 × 5 × 787 is the 85331^th composite number and is not squarefree.
94440 has 4 distinct prime factors, 32 divisors, 19 antidivisors and 25152 totatives.
94440 has a semiprime digit sum 21 in base 10.
94440 has a Fibonacci digit sum 21 in base 10.
94440 has a triangular digit sum 21 in base 10.
94440 = 23611² - 23609² = 11807² - 11803² = 7873² - 7867² = 4727² - 4717² = 3941² - 3929² = 2371² - 2351² = 1589² - 1559² = 817² - 757² is the difference of 2 nonnegative squares in 8 ways.
94440 is the sum of 2 positive triangular numbers.
94440 is the difference of 2 positive pentagonal numbers in 2 ways.
94440 = 10² + 56² + 302² is the sum of 3 positive squares.
94440² = 56664² + 75552² is the sum of 2 positive squares in 1 way.
94440² is the sum of 3 positive squares.
94440 is a proper divisor of 379⁶ - 1.
94440 is palindromic in (at least) the following bases: 86, 89, and 95.

The number 94440 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057280: Coefficient triangle of polynomials (rising powers) related to Fibonacci convolutions. Companion triangle to A057995.
A057282: Coefficient triangle of polynomials (falling powers) related to Fibonacci convolutions. Companion triangle to A057281.
A150180: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 1, -1), (0, 1, 1), (1, -1, -1), (1, 0, 1)}
A208127: Cardinality of the set f^n({s}), where f is a variant of the Collatz function that replaces any element x in the argument set by both x/2 and 3*x+1, and s is an arbitrary irrational number.
A254942: Number of length n 1..(3+1) arrays with every leading partial sum divisible by 2, 3, 5, 7 or 11

Number of the day: 368560735

George Pólya was born on this day 131 years ago.

Properties of the number 368560735:

368560735 is a cyclic number.
368560735 = 5 × 73712147 is semiprime and squarefree.
368560735 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 294848584 totatives.
368560735 has a prime digit sum 43 in base 10.
Reversing the decimal digits of 368560735 results in a prime.
368560735 = 184280368² - 184280367² = 36856076² - 36856071² is the difference of 2 nonnegative squares in 2 ways.
368560735 is the difference of 2 positive pentagonal numbers in 2 ways.
368560735 is not the sum of 3 positive squares.
368560735² = 221136441² + 294848588² is the sum of 2 positive squares in 1 way.
368560735² is the sum of 3 positive squares.
368560735 is a proper divisor of 31^36856073 - 1.
368560735 = '36856073' + '5' is the concatenation of 2 prime numbers.
368560735 = '3685607' + '35' is the concatenation of 2 semiprime numbers.
368560735 = '3685' + '60735' is the concatenation of 2 sphenic numbers.
368560735 is an emirpimes in (at least) the following bases: 11, 13, 19, 24, 25, 37, 45, 46, 47, 51, 53, 63, 64, 73, 77, 79, 85, 87, 92, and 93.

Number of the day: 958492

Properties of the number 958492:

958492 = 2² × 239623 is the 882982^th composite number and is not squarefree.
958492 has 2 distinct prime factors, 6 divisors, 21 antidivisors and 479244 totatives.
958492 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 958492 results in a prime.
958492 = 239624² - 239622² is the difference of 2 nonnegative squares in 1 way.
958492 is the difference of 2 positive pentagonal numbers in 1 way.
958492 is not the sum of 3 positive squares.
958492² is the sum of 3 positive squares.
958492 is a proper divisor of 17³⁹⁹³⁷ - 1.

The number 958492 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A257206: Number of (n+2)X(5+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 and vertically
A257208: Number of (n+2)X(7+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 and vertically

Number of the day: 34260190

Properties of the number 34260190:

34260190 = 2 × 5 × 431 × 7949 is the 32155960^th composite number and is squarefree.
34260190 has 4 distinct prime factors, 16 divisors, 13 antidivisors and 13670560 totatives.
34260190 has a semiprime digit sum 25 in base 10.
34260190 is the difference of 2 positive pentagonal numbers in 3 ways.
34260190 = 445² + 474² + 5817² is the sum of 3 positive squares.
34260190² = 23700690² + 24739400² = 4116912² + 34011934² = 5571106² + 33804192² = 20556114² + 27408152² is the sum of 2 positive squares in 4 ways.
34260190² is the sum of 3 positive squares.
34260190 is a proper divisor of 863⁷⁹⁴⁸ - 1.

Number of the day: 104079

Properties of the number 104079:

104079 = 3 × 34693 is semiprime and squarefree.
104079 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 69384 totatives.
104079 has a semiprime digit sum 21 in base 10.
104079 has a Fibonacci digit sum 21 in base 10.
104079 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 104079 results in an emirpimes.
104079 = 52040² - 52039² = 17348² - 17345² is the difference of 2 nonnegative squares in 2 ways.
104079 is the difference of 2 positive pentagonal numbers in 1 way.
104079 is not the sum of 3 positive squares.
104079² = 61596² + 83895² is the sum of 2 positive squares in 1 way.
104079² is the sum of 3 positive squares.
104079 is a proper divisor of 1489¹² - 1.
104079 = '10407' + '9' is the concatenation of 2 semiprime numbers.
104079 is an emirpimes in (at least) the following bases: 2, 5, 8, 10, 12, 13, 15, 17, 20, 21, 24, 25, 27, 29, 30, 31, 39, 41, 49, 50, 53, 54, 56, 57, 61, 75, 78, and 89.
104079 is palindromic in (at least) the following bases: 93, and -11.

Number of the day: 89568

Properties of the number 89568:

89568 = 2⁵ × 3² × 311 is the 80893^th composite number and is not squarefree.
89568 has 3 distinct prime factors, 36 divisors, 17 antidivisors and 29760 totatives.
89568 has a triangular digit sum 36 in base 10.
89568 is the difference of 2 nonnegative squares in 12 ways.
89568 is the sum of 2 positive triangular numbers.
89568 is the difference of 2 positive pentagonal numbers in 1 way.
89568 = 40² + 52² + 292² is the sum of 3 positive squares.
89568² is the sum of 3 positive squares.
89568 is a proper divisor of 881¹⁰ - 1.

Number of the day: 32383

Properties of the number 32383:

32383 = 13 × 47 × 53 is a sphenic number and squarefree.
32383 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 28704 totatives.
32383 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 32383 results in a semiprime.
32383 = 16192² - 16191² = 1252² - 1239² = 368² - 321² = 332² - 279² is the difference of 2 nonnegative squares in 4 ways.
32383 is the sum of 2 positive triangular numbers.
32383 is the difference of 2 positive pentagonal numbers in 4 ways.
32383 is not the sum of 3 positive squares.
32383² = 17108² + 27495² = 5217² + 31960² = 18800² + 26367² = 12455² + 29892² is the sum of 2 positive squares in 4 ways.
32383² is the sum of 3 positive squares.
32383 is a proper divisor of 659¹² - 1.
32383 = '3' + '2383' is the concatenation of 2 prime numbers.
32383 is palindromic in (at least) the following bases: 8, 32, -2, and -71.
32383 in base 8 = 77177 and consists of only the digits '1' and '7'.
32383 in base 32 = vjv and consists of only the digits 'j' and 'v'.

The number 32383 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A043452: Numbers n such that number of 7's in base 8 is 4.
A049886: a(n)=a(1)+a(2)+...+a(n-1)-a(m), where m=n-1-2^p and 2^p<n-1<=2^(p+1).
A052817: Cycles of rooted trees t where for each t all subtrees at root are distinct. n is total number of nodes.
A070835: Numbers n such that phi(reverse(n)) = sigma(n).
A195460: 2^(2*n+1) - 3*2^n - 1.
A273406: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 673", based on the 5-celled von Neumann neighborhood.
A273833: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 961", based on the 5-celled von Neumann neighborhood.

Number of the day: 7180

Properties of the number 7180:

7180 = 2² × 5 × 359 is the 6262^th composite number and is not squarefree.
7180 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 2864 totatives.
7180 = 1796² - 1794² = 364² - 354² is the difference of 2 nonnegative squares in 2 ways.
7180 is the difference of 2 positive pentagonal numbers in 2 ways.
7180 = 14² + 30² + 78² is the sum of 3 positive squares.
7180² = 4308² + 5744² is the sum of 2 positive squares in 1 way.
7180² is the sum of 3 positive squares.
7180 is a proper divisor of 719² - 1.
7180 is palindromic in (at least) the following bases: 34, 35, 39, -41, -46, and -74.
7180 in base 23 = dd4 and consists of only the digits '4' and 'd'.
7180 in base 33 = 6jj and consists of only the digits '6' and 'j'.
7180 in base 34 = 676 and consists of only the digits '6' and '7'.
7180 in base 35 = 5u5 and consists of only the digits '5' and 'u'.
7180 in base 38 = 4aa and consists of only the digits '4' and 'a'.
7180 in base 39 = 4S4 and consists of only the digits '4' and 'S'.

The number 7180 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000233: Generalized class numbers.
A022266: a(n) = n*(9*n - 1)/2.
A058625: McKay-Thompson series of class 30d for Monster.
A060093: Number of 5-block ordered bicoverings of an unlabeled n-set.
A105282: Positive integers n such that n^20 + 1 is semiprime (A001358).
A130610: Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+359)^2 = y^2.
A134907: a(n) = floor(n*exp(-tan(n))).
A154361: a(n) = 250*n - 70.
A262367: Fixed points of permutations A262323 and A262255.
A285799: Number of partitions of n into parts with an odd number of distinct prime divisors.

Number of the day: 847894

Properties of the number 847894:

847894 = 2 × 19 × 53 × 421 is the 780429^th composite number and is squarefree.
847894 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 393120 totatives.
847894 is the difference of 2 positive pentagonal numbers in 5 ways.
847894 = 2² + 147² + 909² is the sum of 3 positive squares.
847894² = 447944² + 719910² = 397290² + 749056² = 496470² + 687344² = 58406² + 845880² is the sum of 2 positive squares in 4 ways.
847894² is the sum of 3 positive squares.
847894 is a proper divisor of 107³⁰ - 1.

Number of the day: 34801

Nikolai Lobachevsky was born on this day 226 years ago.

Properties of the number 34801:

34801 is a cyclic number.
34801 = 13 × 2677 is semiprime and squarefree.
34801 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 32112 totatives.
Reversing the decimal digits of 34801 results in an emirpimes.
34801 = 17401² - 17400² = 1345² - 1332² is the difference of 2 nonnegative squares in 2 ways.
34801 is the difference of 2 positive pentagonal numbers in 2 ways.
34801 = 49² + 180² = 24² + 185² is the sum of 2 positive squares in 2 ways.
34801 = 4² + 81² + 168² is the sum of 3 positive squares.
34801² = 13385² + 32124² = 8880² + 33649² = 17640² + 29999² = 4745² + 34476² is the sum of 2 positive squares in 4 ways.
34801² is the sum of 3 positive squares.
34801 is a proper divisor of 1033¹² - 1.
34801 = '3' + '4801' is the concatenation of 2 prime numbers.
34801 is an emirpimes in (at least) the following bases: 3, 9, 10, 17, 22, 25, 26, 27, 28, 29, 31, 33, 35, 37, 41, 42, 44, 45, 48, 49, 51, 53, 55, 57, 58, 60, 62, 63, 65, 68, 69, 71, 73, 76, 77, 78, 81, 85, 89, 95, 96, 97, and 100.
34801 is palindromic in (at least) the following bases: 12, -15, and -52.
34801 in base 12 = 18181 and consists of only the digits '1' and '8'.
34801 in base 33 = vvj and consists of only the digits 'j' and 'v'.
34801 in base 51 = DJJ and consists of only the digits 'D' and 'J'.

The number 34801 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020418: Numbers n such that continued fraction for sqrt(n) has period 79.
A135712: a(n) = (4*n^3 + 11*n^2 + 9*n + 2)/2.
A291543: Array read by antidiagonals: T(m,n) = number of maximal irredundant sets in the lattice (rook) graph K_m X K_n.
A303196: Number of nX7 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A303201: Number of 6Xn 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.