Number of the day: 741593

Properties of the number 741593:

741593 is a cyclic number.
741593 is the 59644^th prime.
741593 has 31 antidivisors and 741592 totatives.
741593 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 741593 results in an emirp.
741593 = 54³ + 58³ + 73³ is the sum of 3 positive cubes in 1 way.
741593 = 370797² - 370796² is the difference of 2 nonnegative squares in 1 way.
741593 is the sum of 2 positive triangular numbers.
741593 is the difference of 2 positive pentagonal numbers in 1 way.
741593 = 452² + 733² is the sum of 2 positive squares in 1 way.
741593 = 12² + 43² + 860² is the sum of 3 positive squares.
741593² = 332985² + 662632² is the sum of 2 positive squares in 1 way.
741593² is the sum of 3 positive squares.
741593 is a proper divisor of 47⁹²⁶⁹⁹ - 1.
741593 = '7' + '41593' is the concatenation of 2 prime numbers.
741593 = '7415' + '93' is the concatenation of 2 semiprime numbers.
741593 is an emirp in (at least) the following bases: 7, 10, 18, 26, 28, 40, 49, 55, 57, 76, 84, 85, 88, 93, and 94.

Number of the day: 88655022

Properties of the number 88655022:

88655022 = 2 × 3² × 421 × 11699 is the 83511370^th composite number and is not squarefree.
88655022 has 4 distinct prime factors, 24 divisors, 41 antidivisors and 29478960 totatives.
88655022 has a triangular digit sum 36 in base 10.
88655022 is the sum of 2 positive triangular numbers.
88655022 is the difference of 2 positive pentagonal numbers in 3 ways.
88655022 = 338² + 487² + 9397² is the sum of 3 positive squares.
88655022² = 6106878² + 88444440² is the sum of 2 positive squares in 1 way.
88655022² is the sum of 3 positive squares.
88655022 is a proper divisor of 1663¹⁷⁵⁴⁷ - 1.

Number of the day: 4604

Properties of the number 4604:

4604 = 2² × 1151 is the 3980^th composite number and is not squarefree.
4604 has 2 distinct prime factors, 6 divisors, 15 antidivisors and 2300 totatives.
4604 has a semiprime digit sum 14 in base 10.
4604 = 1152² - 1150² is the difference of 2 nonnegative squares in 1 way.
4604 is the difference of 2 positive pentagonal numbers in 1 way.
4604 is not the sum of 3 positive squares.
4604² is the sum of 3 positive squares.
4604 is a proper divisor of 683¹⁰ - 1.
4604 is palindromic in (at least) the following bases: 18, -43, and -59.
4604 in base 17 = ffe and consists of only the digits 'e' and 'f'.
4604 in base 18 = e3e and consists of only the digits '3' and 'e'.

The number 4604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004112: Numbers n where |cos(n)| (or |cosec(n)| or |cot(n)|) decreases monotonically to 0; also |tan(n)|, |sec(n)|, |sin(n)| increases.
A046964: Sin(n) decreases monotonically to -1.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A065850: Let u be any string of n digits from {0,...,8}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u; then a(n) = max_u f(u).
A066857: Smallest number k such that n! - k is a square
A085329: Non-palindromic solutions to sigma(Rev(n)) = sigma(n).
A139479: Numbers n such that 24n+7 belongs to A000043.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A220681: T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links
A237834: Number of partitions of n such that (greatest part) - (least part) >= number of parts.

Number of the day: 9842

Properties of the number 9842:

9842 = 2 × 7 × 19 × 37 is the 8627^th composite number and is squarefree.
9842 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 3888 totatives.
9842 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 9842 results in a semiprime.
9842 = 4² + 5² + 99² is the sum of 3 positive squares.
9842² = 3192² + 9310² is the sum of 2 positive squares in 1 way.
9842² is the sum of 3 positive squares.
9842 is a proper divisor of 1597⁴ - 1.
9842 = '9' + '842' is the concatenation of 2 semiprime numbers.
9842 is palindromic in (at least) the following bases: 26, 29, 60, -3, -27, -80, and -82.
9842 in base 3 = 111111112 and consists of only the digits '1' and '2'.
9842 in base 24 = h22 and consists of only the digits '2' and 'h'.
9842 in base 26 = eee and consists of only the digit 'e'.
9842 in base 27 = dde and consists of only the digits 'd' and 'e'.
9842 in base 29 = bkb and consists of only the digits 'b' and 'k'.
9842 in base 37 = 770 and consists of only the digits '0' and '7'.
9842 in base 40 = 662 and consists of only the digits '2' and '6'.
9842 in base 49 = 44g and consists of only the digits '4' and 'g'.
9842 in base 59 = 2mm and consists of only the digits '2' and 'm'.
9842 in base 60 = 2i2 and consists of only the digits '2' and 'i'.

The number 9842 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005581: a(n) = (n-1)*n*(n+4)/6.
A007051: a(n) = (3^n + 1)/2.
A047848: Array T read by diagonals; n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is (k+2)^(n-1), for n=1,2,3,...; k=0,1,2,...
A059934: Third step in Goodstein sequences, i.e. g(5) if g(2)=n: write g(4)=A057650(n) in hereditary representation base 4, bump to base 5, then subtract 1 to produce g(5).
A124302: Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
A191450: Dispersion of (3n-1), read by antidiagonals.
A243066: Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
A243506: Permutation of natural numbers: a(n) = A048673(A122111(n)).
A254051: Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
A278984: Array read by antidiagonals downwards: T(b,n) = number of words of length n over an alphabet of size b that are in standard order.

Number of the day: 81140298

Properties of the number 81140298:

81140298 = 2 × 3 × 19 × 711757 is the 76408061^th composite number and is squarefree.
81140298 has 4 distinct prime factors, 16 divisors, 11 antidivisors and 25623216 totatives.
81140298 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 81140298 results in a sphenic number.
81140298 = 95³ + 308³ + 371³ is the sum of 3 positive cubes in 1 way.
81140298 = 32² + 115² + 9007² is the sum of 3 positive squares.
81140298² = 20903610² + 78401448² is the sum of 2 positive squares in 1 way.
81140298² is the sum of 3 positive squares.
81140298 is a proper divisor of 1291⁴⁶⁵² - 1.

Number of the day: 10956

Properties of the number 10956:

10956 = 2² × 3 × 11 × 83 is the 9625^th composite number and is not squarefree.
10956 has 4 distinct prime factors, 24 divisors, 9 antidivisors and 3280 totatives.
10956 has a semiprime digit sum 21 in base 10.
10956 has a Fibonacci digit sum 21 in base 10.
10956 has a triangular digit sum 21 in base 10.
Reversing the decimal digits of 10956 results in a sphenic number.
10956 = 1³ + 16³ + 19³ is the sum of 3 positive cubes in 1 way.
10956 = 2740² - 2738² = 916² - 910² = 260² - 238² = 116² - 50² is the difference of 2 nonnegative squares in 4 ways.
10956 is the sum of 2 positive triangular numbers.
10956 is the difference of 2 positive pentagonal numbers in 1 way.
10956 = 34² + 70² + 70² is the sum of 3 positive squares.
10956² is the sum of 3 positive squares.
10956 is a proper divisor of 331² - 1.
10956 is palindromic in (at least) base -47.
10956 in base 39 = 77a and consists of only the digits '7' and 'a'.
10956 in base 46 = 588 and consists of only the digits '5' and '8'.

The number 10956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A106455: Sequence A106456 interpreted as binary numbers and converted to decimal.
A111533: Row 6 of table A111528.
A114939: Number of essentially different seating arrangements for n couples around a circular table with 2n seats avoiding spouses being neighbors and avoiding clusters of 3 persons with equal gender.
A123862: Expansion of f(q)*f(q^7)/(f(-q)*f(-q^7)) in powers of q where f() is a Ramanujan theta function.
A133242: Indices n such that A134204(n) < n.
A210860: Triangle of coefficients of polynomials u(n,x) jointly generated with A210861; see the Formula section of A210861.
A213818: Antidiagonal sums of the convolution array A213773.
A232137: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order
A281864: Number of sets of exactly four positive integers <= n having a square element sum.
A289227: Number of ways to select 6 disjoint point triples from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.

Number of the day: 94536

Properties of the number 94536:

94536 = 2³ × 3² × 13 × 101 is the 85419^th composite number and is not squarefree.
94536 has 4 distinct prime factors, 48 divisors, 15 antidivisors and 28800 totatives.
94536 has a triangular digit product 3240 in base 10.
94536 is the difference of 2 nonnegative squares in 12 ways.
94536 is the sum of 2 positive triangular numbers.
94536 is the difference of 2 positive pentagonal numbers in 3 ways.
94536 = 90² + 294² = 30² + 306² is the sum of 2 positive squares in 2 ways.
94536 = 16² + 74² + 298² is the sum of 3 positive squares.
94536² = 52920² + 78336² = 36360² + 87264² = 18360² + 92736² = 18720² + 92664² is the sum of 2 positive squares in 4 ways.
94536² is the sum of 3 positive squares.
94536 is a proper divisor of 1009⁴ - 1.
94536 = '9453' + '6' is the concatenation of 2 triangular numbers.
94536 is palindromic in (at least) the following bases: -57, and -95.
94536 in base 56 = U88 and consists of only the digits '8' and 'U'.

The number 94536 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A012698: E.g.f.: sin(arctanh(x)*log(x+1))=2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A012704: arcsinh(arctanh(x)*log(x+1)) = 2/2!*x^2-3/3!*x^3+16/4!*x^4-50/5!*x^5...
A187277: Let S denote the palindromes in the language {0,1,2,...,n-1}*; a(n) = number of words of length 4 in the language SS.
A192770: Numbers n such that n^2 + 1 is divisible by precisely four distinct primes where the sum of the largest and the smallest is equal to the sum of the other two.
A195674: Numbers that are formed using their own digits and addition and seventh power operators.
A199924: Numbers n such that the sum of the largest and the smallest prime divisor of n^2 + 1 equals the sum of the other distinct prime divisors.
A215950: Numbers n > 1 such that the sum of the distinct prime divisors of n^2 + 1 that are congruent to 1 mod 8 equals the sum of the distinct prime divisors congruent to 5 mod 8.