Number of the day: 272017

Godfrey Harold Hardy was born on this day 140 years ago.

Happy e-Day!

Properties of the number 272017:

272017 = 17 × 16001 is semiprime and squarefree.
272017 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 256000 totatives.
272017 has a prime digit sum 19 in base 10.
272017 = 136009² - 136008² = 8009² - 7992² is the difference of 2 nonnegative squares in 2 ways.
272017 is the difference of 2 positive pentagonal numbers in 2 ways.
272017 = 224² + 471² = 24² + 521² is the sum of 2 positive squares in 2 ways.
272017 = 1² + 204² + 480² is the sum of 3 positive squares.
272017² = 171665² + 211008² = 128008² + 240015² = 25008² + 270865² = 105400² + 250767² is the sum of 2 positive squares in 4 ways.
272017² is the sum of 3 positive squares.
272017 is a divisor of 83¹⁶ - 1.
272017 is an emirpimes in (at least) the following bases: 2, 6, 7, 9, 11, 12, 13, 15, 17, 19, 20, 22, 25, 26, 29, 31, 33, 35, 37, 39, 41, 43, 47, 48, 49, 51, 53, 55, 56, 59, 60, 62, 70, 71, 73, 74, 76, 78, 79, 81, 85, 87, 89, 91, 95, and 96.
272017 is palindromic in (at least) base -97.

Number of the day: 956

Properties of the number 956:

956 = 2² × 239 is the 793^th composite number and is not squarefree.
956 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 476 totatives.
956 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 956 results in a prime.
956 = 240² - 238² is the difference of 2 nonnegative squares in 1 way.
956 is the sum of 2 positive triangular numbers.
956 is the difference of 2 positive pentagonal numbers in 1 way.
956 is not the sum of 3 positive squares.
956² is the sum of 3 positive squares.
956 is a divisor of 479² - 1.
956 = '95' + '6' is the concatenation of 2 semiprime numbers.
956 is palindromic in (at least) the following bases: 14, 18, and -17.
956 in base 14 = 4c4 and consists of only the digits '4' and 'c'.
956 in base 18 = 2h2 and consists of only the digits '2' and 'h'.
956 in base 30 = 11q and consists of only the digits '1' and 'q'.

The number 956 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003480: a(n) = 4a(n-1) - 2a(n-2) (n >= 3).
A006313: Numbers n such that n^16 + 1 is prime.
A006314: Numbers n such that n^8 + 1 is prime.
A023359: Number of compositions (ordered partitions) of n into powers of 2.
A060978: |First digit - second digit + third digit - fourth digit ...| = 10.
A087097: Lunar primes (formerly called dismal primes) (cf. A087062).
A161424: Numbers n such that their largest divisor <= sqrt(n) equals 4.
A231145: Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 5 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=n-n%2, read by rows.
A235229: Numbers whose sum of digits is 20.
A238557: Number T(n,k) of equivalence classes of ways of placing k 2 X 2 tiles in an n X 8 rectangle under all symmetry operations of the rectangle; irregular triangle T(n,k), n>=2, 0<=k<=4*floor(n/2), read by rows.

Number of the day: 491587949916

Properties of the number 491587949916:

491587949916 = 2² × 3⁴ × 7 × 216749537 is composite and not squarefree.
491587949916 has 4 distinct prime factors, 60 divisors, 25 antidivisors and 140453699328 totatives.
491587949916 has an oblong digit sum 72 in base 10.
491587949916 is the difference of 2 nonnegative squares in 10 ways.
491587949916 is the difference of 2 positive pentagonal numbers in 2 ways.
491587949916 is not the sum of 3 positive squares.
491587949916² = 139041611100² + 471514732416² is the sum of 2 positive squares in 1 way.
491587949916² is the sum of 3 positive squares.
491587949916 is a divisor of 1567^40640538 - 1.

Number of the day: 92645

Properties of the number 92645:

92645 = 5 × 7 × 2647 is a sphenic number and squarefree.
92645 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 63504 totatives.
92645 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 92645 results in a prime.
92645 = (190 × 191)/2 + … + (194 × 195)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
92645 = 46323² - 46322² = 9267² - 9262² = 6621² - 6614² = 1341² - 1306² is the difference of 2 nonnegative squares in 4 ways.
92645 is the difference of 2 positive pentagonal numbers in 4 ways.
92645 = 2² + 15² + 304² is the sum of 3 positive squares.
92645² = 55587² + 74116² is the sum of 2 positive squares in 1 way.
92645² is the sum of 3 positive squares.
92645 is a divisor of 241¹⁸ - 1.
92645 is palindromic in (at least) base -97.

The number 92645 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A205483: L.g.f.: Sum_{n>=1} x^n/n * Product_{d|n} (1 + d*x^n)^d.
A239429: Numbers n such that n^6+6 and n^6-6 are prime.

Number of the day: 425448

Gaston Julia was born on this day 124 years ago.

Properties of the number 425448:

425448 = 2³ × 3² × 19 × 311 is the 389632^th composite number and is not squarefree.
425448 has 4 distinct prime factors, 48 divisors, 13 antidivisors and 133920 totatives.
425448 is the difference of 2 nonnegative squares in 12 ways.
425448 is the sum of 2 positive triangular numbers.
425448 is the difference of 2 positive pentagonal numbers in 3 ways.
425448 = 104² + 194² + 614² is the sum of 3 positive squares.
425448² is the sum of 3 positive squares.
425448 is a divisor of 1867¹⁸ - 1.
425448 in base 47 = 44S4 and consists of only the digits '4' and 'S'.

Number of the day: 299096

Bartel Leendert van der Waerden was born on this day 114 years ago.

Properties of the number 299096:

299096 = 2³ × 7³ × 109 is the 273168^th composite number and is not squarefree.
299096 has 3 distinct prime factors, 32 divisors, 13 antidivisors and 127008 totatives.
299096 has a semiprime digit sum 35 in base 10.
299096 = 74775² - 74773² = 37389² - 37385² = 10689² - 10675² = 5355² - 5327² = 1575² - 1477² = 861² - 665² = 795² - 577² = 561² - 125² is the difference of 2 nonnegative squares in 8 ways.
299096 = 36² + 130² + 530² is the sum of 3 positive squares.
299096² = 164640² + 249704² is the sum of 2 positive squares in 1 way.
299096² is the sum of 3 positive squares.
299096 is a divisor of 19³⁶ - 1.
299096 = '29909' + '6' is the concatenation of 2 semiprime numbers.

The number 299096 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A204088: Row sums of A204087.

Number of the day: 50777603889348

John Napier was born on this day 467 years ago.

John Napier was born on this day 467 years ago.

Properties of the number 50777603889348:

50777603889348 = 2² × 3 × 7 × 17 × 79 × 733 × 614063 is composite and not squarefree.
50777603889348 has 7 distinct prime factors, 192 divisors, 107 antidivisors and 13463225837568 totatives.
Reversing the decimal digits of 50777603889348 results in a sphenic number.
50777603889348 is the difference of 2 nonnegative squares in 32 ways.
50777603889348 is the difference of 2 positive pentagonal numbers in 14 ways.
50777603889348 = 3664² + 14926² + 7125824² is the sum of 3 positive squares.
50777603889348² = 30235921744560² + 40794044822748² = 23895343006752² + 44803768137660² = 17033174244240² + 47835510156252² = 7481556916848² + 50223414488100² is the sum of 2 positive squares in 4 ways.
50777603889348² is the sum of 3 positive squares.
50777603889348 is a divisor of 1579^7368744 - 1.