Number of the day: 6971

Properties of the number 6971:

6971 is a cyclic number.
6971 is the 896^th prime.
6971 has 7 antidivisors and 6970 totatives.
6971 has a prime digit sum 23 in base 10.
6971 has a triangular digit product 378 in base 10.
6971 has sum of divisors equal to 6972 which is an oblong number.
6971 = 3486² - 3485² is the difference of 2 nonnegative squares in 1 way.
6971 is the difference of 2 positive pentagonal numbers in 1 way.
6971 = 1² + 9² + 83² is the sum of 3 positive squares.
6971² is the sum of 3 positive squares.
6971 is a proper divisor of 1279³⁴ - 1.
6971 is an emirp in (at least) the following bases: 4, 5, 7, 9, 13, 15, 19, 23, 29, 30, 31, 39, 41, 43, 53, 55, 57, 60, 61, 64, 69, 70, 73, 74, 75, 77, 79, 81, 83, 85, 89, 90, 91, 92, 97, and 99.
6971 is palindromic in (at least) the following bases: 82, -10, -35, -52, -69, and -85.
6971 in base 13 = 3233 and consists of only the digits '2' and '3'.
6971 in base 29 = 88b and consists of only the digits '8' and 'b'.
6971 in base 31 = 77r and consists of only the digits '7' and 'r'.
6971 in base 34 = 611 and consists of only the digits '1' and '6'.

The number 6971 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002148: Smallest prime p==3 (mod 8) such that Q(sqrt(-p)) has class number 2n+1.
A002327: Primes of the form k^2 - k - 1.
A057186: Numbers n such that (20^n+1)/21 is a prime.
A059236: Primes p such that x^41 = 2 has no solution mod p.
A082108: a(n) = 4n^2 + 6n + 1.
A089299: Number of square plane partitions of n.
A127341: Primes that can be written as the sum of 13 consecutive primes.
A136079: Father primes of order 10.
A141908: Primes congruent to 2 mod 23.
A153377: Larger of two consecutive prime numbers such that p1*p2*d + d = average of twin prime pairs, d (delta) = p2 - p1.

Number of the day: 2717

Otto Toeplitz was born on this day 141 years ago.

Properties of the number 2717:

2717 is a cyclic number.
2717 = 11 × 13 × 19 is a sphenic number and squarefree.
2717 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 2160 totatives.
2717 has an emirp digit sum 17 in base 10.
2717 = 2³ + 8³ + 13³ is the sum of 3 positive cubes in 1 way.
2717 = 14³ - 3³ is the difference of 2 positive cubes in 1 way.
2717 = 1359² - 1358² = 129² - 118² = 111² - 98² = 81² - 62² is the difference of 2 nonnegative squares in 4 ways.
2717 is the difference of 2 positive pentagonal numbers in 4 ways.
2717 = 2² + 3² + 52² is the sum of 3 positive squares.
2717² = 1045² + 2508² is the sum of 2 positive squares in 1 way.
2717² is the sum of 3 positive squares.
2717 is a proper divisor of 571² - 1.
2717 = '271' + '7' is the concatenation of 2 prime numbers.
2717 is palindromic in (at least) the following bases: -24, and -97.
2717 in base 23 = 533 and consists of only the digits '3' and '5'.

The number 2717 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000914: Stirling numbers of the first kind: s(n+2, n).
A033680: a(1) = 1; a(n) is smallest number >= a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A045947: Triangles in open triangular matchstick arrangement (triangle minus one side) of side n.
A054333: 1/256 of tenth unsigned column of triangle A053120 (T-Chebyshev, rising powers, zeros omitted).
A082985: Coefficient table for Chebyshev's U(2*n,x) polynomial expanded in decreasing powers of (-4*(1-x^2)).
A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
A185589: Iterate the map in A006369 starting at 144.
A216169: Composite numbers > 9 which yield a prime whenever a 0 is inserted between any two digits.
A297720: T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.
A319721: Number of non-isomorphic antichains of multisets of weight n.

Number of the day: 629046

Properties of the number 629046:

629046 = 2 × 3⁴ × 11 × 353 is the 577774^th composite number and is not squarefree.
629046 has 4 distinct prime factors, 40 divisors, 23 antidivisors and 190080 totatives.
629046 = 1² + 14² + 793² is the sum of 3 positive squares.
629046² = 400950² + 484704² is the sum of 2 positive squares in 1 way.
629046² is the sum of 3 positive squares.
629046 is a proper divisor of 647¹⁶⁰ - 1.
629046 = '62' + '9046' is the concatenation of 2 semiprime numbers.

Number of the day: 202917

Properties of the number 202917:

202917 = 3 × 11² × 13 × 43 is the 184699^th composite number and is not squarefree.
202917 has 4 distinct prime factors, 24 divisors, 31 antidivisors and 110880 totatives.
202917 has a semiprime digit sum 21 in base 10.
202917 has a Fibonacci digit sum 21 in base 10.
202917 has a triangular digit sum 21 in base 10.
202917 is the difference of 2 nonnegative squares in 12 ways.
202917 is the sum of 2 positive triangular numbers.
202917 is the difference of 2 positive pentagonal numbers in 5 ways.
202917 = 2² + 47² + 448² is the sum of 3 positive squares.
202917² = 78045² + 187308² is the sum of 2 positive squares in 1 way.
202917² is the sum of 3 positive squares.
202917 is a proper divisor of 727¹⁴ - 1.
202917 = '2029' + '17' is the concatenation of 2 prime numbers.
202917 = '202' + '917' is the concatenation of 2 semiprime numbers.
202917 is palindromic in (at least) the following bases: -60, and -62.
202917 in base 32 = 6655 and consists of only the digits '5' and '6'.
202917 in base 34 = 55i5 and consists of only the digits '5' and 'i'.

The number 202917 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A218266: Number of standard Young tableaux of n cells and height >= 6.

Number of the day: 7793

Properties of the number 7793:

7793 is a cyclic number.
7793 is the 987^th prime.
7793 has 13 antidivisors and 7792 totatives.
7793 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7793 results in a semiprime.
7793 = 3897² - 3896² is the difference of 2 nonnegative squares in 1 way.
7793 is the difference of 2 positive pentagonal numbers in 1 way.
7793 = 7² + 88² is the sum of 2 positive squares in 1 way.
7793 = 6² + 19² + 86² is the sum of 3 positive squares.
7793² = 1232² + 7695² is the sum of 2 positive squares in 1 way.
7793² is the sum of 3 positive squares.
7793 is a proper divisor of 43⁴⁸⁷ - 1.
7793 = '77' + '93' is the concatenation of 2 semiprime numbers.
7793 is an emirp in (at least) the following bases: 3, 4, 5, 11, 16, 20, 21, 23, 24, 27, 31, 41, 49, 55, 59, 61, 63, 64, 67, 70, 80, 83, 84, 85, 86, 95, 98, and 100.
7793 is palindromic in (at least) the following bases: 28, 53, -34, and -44.
7793 in base 28 = 9q9 and consists of only the digits '9' and 'q'.
7793 in base 33 = 755 and consists of only the digits '5' and '7'.
7793 in base 52 = 2jj and consists of only the digits '2' and 'j'.
7793 in base 53 = 2f2 and consists of only the digits '2' and 'f'.

The number 7793 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001134: Primes p such that the multiplicative order of 2 modulo p is (p-1)/4.
A051026: Number of primitive subsequences of {1, 2, ..., n}.
A057622: Initial prime in first sequence of n consecutive primes congruent to 5 modulo 6.
A068652: Numbers such that every cyclic permutation is a prime.
A128337: Numbers k such that (7^k + 5^k)/12 is prime.
A142200: Primes congruent to 3 mod 41.
A154577: Primes of the form 2n^2+14n+5.
A293663: Circular primes that are not repunits.
A316652: Number of series-reduced rooted trees whose leaves span an initial interval of positive integers with multiplicities an integer partition of n.
A317716: Square array A(n, k), read by antidiagonals downwards: k-th prime p such that cyclic digit shifts produce exactly n different primes.

Number of the day: 75335

Ernst Friedrich Ferdinand Zermelo was born on this day 151 years ago.

Properties of the number 75335:

75335 = 5 × 13 × 19 × 61 is the 67912^th composite number and is squarefree.
75335 has 4 distinct prime factors, 16 divisors, 21 antidivisors and 51840 totatives.
75335 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 75335 results in a semiprime.
75335 = 37668² - 37667² = 7536² - 7531² = 2904² - 2891² = 1992² - 1973² = 648² - 587² = 612² - 547² = 444² - 349² = 276² - 29² is the difference of 2 nonnegative squares in 8 ways.
75335 is the difference of 2 positive pentagonal numbers in 7 ways.
75335 is not the sum of 3 positive squares.
75335² = 45201² + 60268² = 33592² + 67431² = 51129² + 55328² = 18544² + 73017² = 5073² + 75164² = 31407² + 68476² = 38247² + 64904² = 25916² + 70737² = 49324² + 56943² = 28975² + 69540² = 15960² + 73625² = 41040² + 63175² = 13585² + 74100² is the sum of 2 positive squares in 13 ways.
75335² is the sum of 3 positive squares.
75335 is a proper divisor of 1559¹⁰ - 1.
75335 = '753' + '35' is the concatenation of 2 semiprime numbers.
75335 is palindromic in (at least) base 70.
75335 in base 58 = MMp and consists of only the digits 'M' and 'p'.

The number 75335 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A132124: a(n) = n*(n+1)*(8*n + 1)/6.
A137080: Numbers k such that k and k^2 use only the digits 2, 3, 5, 6 and 7.
A345705: Numbers k such that (3^ord(3/2, k) - 2^ord(3/2, k))/k is a prime, where ord(3/2, k) is the multiplicative order of 3/2 (mod k).

Number of the day: 3430

Properties of the number 3430:

3430 = 2 × 5 × 7³ is the 2949^th composite number and is not squarefree.
3430 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 1176 totatives.
3430 has a semiprime digit sum 10 in base 10.
3430 has a triangular digit sum 10 in base 10.
3430 = 7³ + 7³ + 14³ is the sum of 3 positive cubes in 1 way.
3430 is the sum of 2 positive triangular numbers.
3430 is the difference of 2 positive pentagonal numbers in 4 ways.
3430 = 9² + 10² + 57² is the sum of 3 positive squares.
3430² = 2058² + 2744² is the sum of 2 positive squares in 1 way.
3430² is the sum of 3 positive squares.
3430 is a proper divisor of 1373⁴ - 1.
3430 is palindromic in (at least) the following bases: 18, 21, 25, 69, 97, and -19.
3430 in base 16 = d66 and consists of only the digits '6' and 'd'.
3430 in base 18 = aaa and consists of only the digit 'a'.
3430 in base 19 = 99a and consists of only the digits '9' and 'a'.
3430 in base 21 = 7g7 and consists of only the digits '7' and 'g'.
3430 in base 24 = 5mm and consists of only the digits '5' and 'm'.
3430 in base 25 = 5c5 and consists of only the digits '5' and 'c'.
3430 in base 58 = 118 and consists of only the digits '1' and '8'.

The number 3430 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007727: Number of 2n-bead black-white strings with n black beads and fundamental period 2n.
A025632: Numbers of form 7^i*10^j, with i, j >= 0.
A027466: Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j).
A027474: a(n) = 7^(n-2) * C(n,2).
A051682: 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n-7)/2.
A088409: a(n) = A063416(n)/7.
A208688: T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically
A241638: Number of partitions p of n such that (number of even numbers in p) = (number of odd numbers in p).
A325793: Positive integers whose number of divisors is equal to their sum of prime indices.
A351255: Numbers whose k-th arithmetic derivative is zero for some k>0, ordered by their position in A276086.