Tuesday, February 21, 2017

Number of the day: 354158497701

Properties of the number 354158497701:

354158497701 = 32 × 97 × 405679837 is composite and not squarefree.
354158497701 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 233671585536 totatives.
354158497701 = 1770792488512 - 1770792488502 = 590264162852 - 590264162822 = 196754720992 - 196754720902 = 18255593152 - 18255592182 = 6085199012 - 6085196102 = 2028403552 - 2028394822 is the difference of 2 nonnegative squares in 6 ways.
354158497701 is the difference of 2 positive pentagonal numbers in 2 ways.
354158497701 = 4011902 + 4395512 = 574262 + 5923352 is the sum of 2 positive squares in 2 ways.
354158497701 = 792 + 4462 + 5951122 is the sum of 3 positive squares.
3541584977012 = 2373227046452 + 2628805343762 = 680308594202 + 3475630067492 = 322516655012 + 3526869313802 = 2123972229242 + 2834001785252 is the sum of 2 positive squares in 4 ways.
3541584977012 is the sum of 3 positive squares.
354158497701 is a divisor of 1093445264 - 1.
354158497701 = '35' + '4158497701' is the concatenation of 2 semiprime numbers.

Monday, February 20, 2017

Number of the day: 361394

Properties of the number 361394:

361394 = 2 × 11 × 16427 is a sphenic number and squarefree.
361394 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 164260 totatives.
361394 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 361394 results in a sphenic number.
361394 is the difference of 2 positive pentagonal numbers in 2 ways.
361394 = 72 + 122 + 6012 is the sum of 3 positive squares.
3613942 is the sum of 3 positive squares.
361394 is a divisor of 1277191 - 1.
361394 = '361' + '394' is the concatenation of 2 semiprime numbers.
361394 is palindromic in (at least) base 90.

Sunday, February 19, 2017

Number of the day: 7127

Properties of the number 7127:

7127 and 7129 form a twin prime pair.
7127 has 5 antidivisors and 7126 totatives.
7127 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 7127 results in a semiprime.
7127 = 35642 - 35632 is the difference of 2 nonnegative squares in 1 way.
7127 is the difference of 2 positive pentagonal numbers in 1 way.
7127 is not the sum of 3 positive squares.
71272 is the sum of 3 positive squares.
7127 is a divisor of 3509 - 1.
7127 = '7' + '127' is the concatenation of 2 prime numbers.
7127 is an emirp in (at least) the following bases: 2, 6, 7, 11, 13, 18, 19, 20, 21, 25, 37, 39, 41, 43, 49, 53, 55, 60, 65, 76, 84, 85, 90, and 93.
7127 is palindromic in (at least) the following bases: 57, -52, and -75.
7127 in base 6 = 52555 and consists of only the digits '2' and '5'.
7127 in base 13 = 3323 and consists of only the digits '2' and '3'.
7127 in base 56 = 2FF and consists of only the digits '2' and 'F'.
7127 in base 57 = 2B2 and consists of only the digits '2' and 'B'.
7127 in base 59 = 22l and consists of only the digits '2' and 'l'.

The number 7127 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000945: Euclid-Mullin sequence: a(1) = 2, a(n+1) is smallest prime factor of 1 + Product_{k=1..n} a(k).
A045713: Primes with first digit 7.
A050268: Primes of the form 36*n^2 - 810*n + 2753, listed in order of increasing parameter n >= 0.
A090287: Smallest prime obtained by sandwiching n between a number with identical digits, or 0 if no such prime exists. Primes of the form k n k where all the digits of k are identical.
A129658: Numerators of the convergents of the continued fraction for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
A134971: Canyon primes.
A136074: Father primes of order 5.
A174913: Lesser of twin primes p1 such that 2*p1+p2 is a prime number.
A204867: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly two different ways, and new values 0..1 introduced in row major order
A263358: Expansion of Product_{k>=1} 1/(1-x^(k+2))^k.

Friday, February 17, 2017

Number of the day: 803782

Properties of the number 803782:

803782 = 2 × 7 × 57413 is a sphenic number and squarefree.
803782 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 344472 totatives.
803782 has a triangular digit sum 28 in base 10.
803782 is the difference of 2 positive pentagonal numbers in 4 ways.
803782 = 102 + 992 + 8912 is the sum of 3 positive squares.
8037822 = 2391902 + 7673682 is the sum of 2 positive squares in 1 way.
8037822 is the sum of 3 positive squares.
803782 is a divisor of 18162 - 1.
803782 is palindromic in (at least) base -98.

Thursday, February 16, 2017

Number of the day: 118176156951

Properties of the number 118176156951:

118176156951 = 3 × 83617 × 471101 is a sphenic number and squarefree.
118176156951 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 78782995200 totatives.
118176156951 has an emirpimes digit sum 51 in base 10.
118176156951 = 590880784762 - 590880784752 = 196960261602 - 196960261572 = 7484602 - 6648432 = 3609762 - 1101252 is the difference of 2 nonnegative squares in 4 ways.
118176156951 is the sum of 2 positive triangular numbers.
118176156951 is the difference of 2 positive pentagonal numbers in 1 way.
118176156951 is not the sum of 3 positive squares.
1181761569512 = 668486464652 + 974518472762 = 599353536242 + 1018496806952 = 111208598762 + 1176517341452 = 500849106602 + 1070378708492 is the sum of 2 positive squares in 4 ways.
1181761569512 is the sum of 3 positive squares.
118176156951 is a divisor of 11232164368 - 1.
118176156951 = '118' + '176156951' is the concatenation of 2 semiprime numbers.

Wednesday, February 15, 2017

Number of the day: 40573506153901

Galileo Galilei was born on this day 453 years ago.

Alfred North Whitehead was born on this day 156 years ago.

Properties of the number 40573506153901:

40573506153901 = 7 × 151 × 421 × 91177033 is composite and squarefree.
40573506153901 has 4 distinct prime factors, 16 divisors, 47 antidivisors and 34464918096000 totatives.
40573506153901 has an emirpimes digit sum 49 in base 10.
40573506153901 = 202867530769512 - 202867530769502 = 28981075824252 - 28981075824182 = 1343493582012 - 1343493580502 = 481870621512 - 481870617302 = 191927659752 - 191927649182 = 68838674652 - 68838645182 = 3191514012 - 3190878302 = 458110152 - 453660182 is the difference of 2 nonnegative squares in 8 ways.
40573506153901 is the sum of 2 positive triangular numbers.
40573506153901 is the difference of 2 positive pentagonal numbers in 8 ways.
40573506153901 = 79402 + 354512 + 63696302 is the sum of 3 positive squares.
405735061539012 = 216507024792242 + 343140857925252 = 192355975137552 + 357239582060762 = 239629537512052 + 327412010949242 = 27948495925492 + 404771320300202 is the sum of 2 positive squares in 4 ways.
405735061539012 is the sum of 3 positive squares.
40573506153901 is a divisor of 166356985645 - 1.

Tuesday, February 14, 2017

Number of the day: 369685

Properties of the number 369685:

369685 = 5 × 107 × 691 is a sphenic number and squarefree.
369685 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 292560 totatives.
369685 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 369685 results in a sphenic number.
369685 = 1848432 - 1848422 = 369712 - 369662 = 17812 - 16742 = 6132 - 782 is the difference of 2 nonnegative squares in 4 ways.
369685 is the sum of 2 positive triangular numbers.
369685 is the difference of 2 positive pentagonal numbers in 3 ways.
369685 = 1612 + 1802 + 5582 is the sum of 3 positive squares.
3696852 = 2218112 + 2957482 is the sum of 2 positive squares in 1 way.
3696852 is the sum of 3 positive squares.
369685 is a divisor of 1381106 - 1.
369685 is palindromic in (at least) base 95.
369685 in base 58 = 1ppp and consists of only the digits '1' and 'p'.