Number of the day: 1509

Hermann Minkowski was born on this day 153 years ago.

Properties of the number 1509:

1509 is a cyclic number.
1509 = 3 × 503 is semiprime and squarefree.
1509 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 1004 totatives.
1509 has an emirpimes digit sum 15 in base 10.
1509 has a triangular digit sum 15 in base 10.
1509 has sum of divisors equal to 2016 which is a triangular number.
Reversing the decimal digits of 1509 results in a sphenic number.
1509 = 755² - 754² = 253² - 250² is the difference of 2 nonnegative squares in 2 ways.
1509 is the sum of 2 positive triangular numbers.
1509 is the difference of 2 positive pentagonal numbers in 1 way.
1509 = 8² + 17² + 34² is the sum of 3 positive squares.
1509² is the sum of 3 positive squares.
1509 is a proper divisor of 7²⁵¹ - 1.
1509 is an emirpimes in (at least) the following bases: 4, 6, 9, 11, 12, 15, 18, 19, 20, 22, 24, 32, 36, 38, 41, 42, 47, 49, 55, 57, 59, 60, 64, 65, 71, 75, 77, 83, 84, 87, 91, 93, 96, 98, and 99.
1509 is palindromic in (at least) the following bases: 16, 29, -52, and -58.
1509 in base 16 = 5e5 and consists of only the digits '5' and 'e'.
1509 in base 28 = 1pp and consists of only the digits '1' and 'p'.
1509 in base 29 = 1n1 and consists of only the digits '1' and 'n'.
1509 in base 38 = 11R and consists of only the digits '1' and 'R'.

The number 1509 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005228: Sequence and first differences (A030124) together list all positive numbers exactly once.
A006832: Discriminants of totally real cubic fields.
A026105: Triangle T read by rows: differences of Motzkin triangle (A026300).
A059993: Pinwheel numbers: a(n) = 2*n^2 + 6*n + 1.
A094612: Fundamental discriminants of real quadratic number fields with class number 3.
A165652: Number of disconnected 2-regular graphs on n vertices.
A202124: T(n,k)=Number of -k..k arrays of n elements with first, second and third differences also in -k..k
A224146: T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing
A241306: T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4
A279567: Number of length n inversion sequences avoiding the patterns 100, 110, 120, and 210.

Number of the day: 9348

Properties of the number 9348:

9348 = 2² × 3 × 19 × 41 is the 8190^th composite number and is not squarefree.
9348 has 4 distinct prime factors, 24 divisors, 11 antidivisors and 2880 totatives.
Reversing the decimal digits of 9348 results in a sphenic number.
9348 = 2338² - 2336² = 782² - 776² = 142² - 104² = 98² - 16² is the difference of 2 nonnegative squares in 4 ways.
9348 is the sum of 2 positive triangular numbers.
9348 is the difference of 2 positive pentagonal numbers in 1 way.
9348 = 2² + 40² + 88² is the sum of 3 positive squares.
9348² = 2052² + 9120² is the sum of 2 positive squares in 1 way.
9348² is the sum of 3 positive squares.
9348 is a proper divisor of 1559² - 1.
9348 is palindromic in (at least) the following bases: -13, -22, -26, and -33.
9348 in base 25 = enn and consists of only the digits 'e' and 'n'.
9348 in base 32 = 944 and consists of only the digits '4' and '9'.
9348 in base 36 = 77o and consists of only the digits '7' and 'o'.

The number 9348 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001610: a(n) = a(n-1) + a(n-2) + 1.
A031367: Inflation orbit counts.
A099925: a(n) = Lucas(n) + (-1)^n.
A120019: Square table, read by antidiagonals, of self-compositions of A120010.
A120020: Coefficients of x^n in the n-th iteration of the g.f. of A120010: a(n) = [x^n] { (1-sqrt(1-4*x))/2 o x/(1-n*x) o (x-x^2) } for n>=1.
A179249: Numbers n that have 9 terms in their Zeckendorf representation.
A197218: Phi(Lucas(n)).
A209796: T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly one duplicate clockwise edge difference
A214980: Positions of zeros in A214979.
A231089: Initial members of abundant quadruplets, i.e., values of n such that (n, n+2, n+4, n+6) are all abundant numbers.

Number of the day: 746010

Properties of the number 746010:

746010 = 2 × 3⁵ × 5 × 307 is the 686066^th composite number and is not squarefree.
746010 has 4 distinct prime factors, 48 divisors, 25 antidivisors and 198288 totatives.
746010 = 20³ + 43³ + 87³ = 42³ + 63³ + 75³ is the sum of 3 positive cubes in 2 ways.
746010 is the difference of 2 positive pentagonal numbers in 1 way.
746010 = 55² + 124² + 853² is the sum of 3 positive squares.
746010² = 447606² + 596808² is the sum of 2 positive squares in 1 way.
746010² is the sum of 3 positive squares.
746010 is a proper divisor of 631²⁷ - 1.
746010 is palindromic in (at least) base -97.

Number of the day: 641

Blaise Pascal was born on this day 394 years ago.

Properties of the number 641:

641 is a cyclic number.
641 and 643 form a twin prime pair.
641 has 7 antidivisors and 640 totatives.
641 has a prime digit sum 11 in base 10.
641 has sum of divisors equal to 642 which is a sphenic number.
Reversing the decimal digits of 641 results in a semiprime.
641 = 321² - 320² is the difference of 2 nonnegative squares in 1 way.
641 is the difference of 2 positive pentagonal numbers in 1 way.
641 = 4² + 25² is the sum of 2 positive squares in 1 way.
641 = 6² + 11² + 22² is the sum of 3 positive squares.
641² = 200² + 609² is the sum of 2 positive squares in 1 way.
641² is the sum of 3 positive squares.
641 is a proper divisor of 487⁴ - 1.
641 is an emirp in (at least) the following bases: 3, 9, 11, 13, 15, 22, 27, 29, 36, 37, 45, 47, 48, 53, 54, 57, 59, 61, 71, 75, 77, 79, 82, 83, 85, 86, 87, 88, 89, and 90.
641 is palindromic in (at least) the following bases: 20, -12, -13, -32, -40, -64, and -80.
641 in base 11 = 533 and consists of only the digits '3' and '5'.
641 in base 12 = 455 and consists of only the digits '4' and '5'.
641 in base 14 = 33b and consists of only the digits '3' and 'b'.
641 in base 19 = 1ee and consists of only the digits '1' and 'e'.
641 in base 20 = 1c1 and consists of only the digits '1' and 'c'.

The number 641 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001097: Twin primes.
A001359: Lesser of twin primes.
A005384: Sophie Germain primes p: 2p+1 is also prime.
A005846: Primes of the form n^2 + n + 41.
A007519: Primes of form 8n+1, that is, primes congruent to 1 mod 8.
A023201: Sexy primes: numbers n such that n and n + 6 are both prime.
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.
A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.
A212959: Number of (w,x,y) such that w,x,y are all in {0,...,n} and |w-x| = |x-y|.
A235266: Primes whose base 2 representation is also the base 3 representation of a prime.

Number of the day: 53982

Properties of the number 53982:

53982 = 2 × 3² × 2999 is the 48483^th composite number and is not squarefree.
53982 has 3 distinct prime factors, 12 divisors, 21 antidivisors and 17988 totatives.
53982 is the difference of 2 positive pentagonal numbers in 2 ways.
53982 = 38² + 53² + 223² is the sum of 3 positive squares.
53982² is the sum of 3 positive squares.
53982 is a proper divisor of 73¹⁴⁹⁹ - 1.
53982 is palindromic in (at least) the following bases: 85, -45, and -70.
53982 in base 44 = Rcc and consists of only the digits 'R' and 'c'.

The number 53982 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A249058: a(n) = number of primes less than the square root of the (2^n)-th prime

Number of the day: 580667

Properties of the number 580667:

580667 is a cyclic number.
580667 = 29 × 20023 is semiprime and squarefree.
580667 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 560616 totatives.
580667 = 290334² - 290333² = 10026² - 9997² is the difference of 2 nonnegative squares in 2 ways.
580667 is the difference of 2 positive pentagonal numbers in 2 ways.
580667 = 5² + 39² + 761² is the sum of 3 positive squares.
580667² = 400460² + 420483² is the sum of 2 positive squares in 1 way.
580667² is the sum of 3 positive squares.
580667 is a proper divisor of 563⁵⁶⁴ - 1.
580667 is an emirpimes in (at least) the following bases: 2, 3, 5, 6, 9, 11, 13, 18, 19, 23, 24, 27, 29, 32, 38, 42, 48, 49, 53, 60, 67, 68, 71, 72, 73, 74, 76, 79, 84, 87, 89, 90, 94, and 98.
580667 is palindromic in (at least) base -93.

The number 580667 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A244246: Number of partitions of n into 10 parts such that every i-th smallest part (counted with multiplicity) is different from i.

Number of the day: 92756230379

Properties of the number 92756230379:

92756230379 is a cyclic number.
92756230379 = 1231 × 75350309 is semiprime and squarefree.
92756230379 has 2 distinct prime factors, 4 divisors, 33 antidivisors and 92680878840 totatives.
92756230379 has a prime digit sum 53 in base 10.
Reversing the decimal digits of 92756230379 results in a sphenic number.
92756230379 = 46378115190² - 46378115189² = 37675770² - 37674539² is the difference of 2 nonnegative squares in 2 ways.
92756230379 is the difference of 2 positive pentagonal numbers in 2 ways.
92756230379 = 973² + 1993² + 304551² is the sum of 3 positive squares.
92756230379² = 40056075260² + 83661395571² is the sum of 2 positive squares in 1 way.
92756230379² is the sum of 3 positive squares.
92756230379 is a proper divisor of 127^20550084 - 1.
92756230379 = '9' + '2756230379' is the concatenation of 2 semiprime numbers.
92756230379 is an emirpimes in (at least) the following bases: 2, 5, 6, 9, 11, 13, 17, 20, 22, 23, 26, 36, 43, 48, 50, 54, 60, 61, 62, 64, 69, 71, 74, 77, 81, 88, 95, 96, and 100.