Monday, October 31, 2016

Number of the day: 214239

Karl Weierstrass was born on this day 201 years ago.

Properties of the number 214239:

214239 = 3 × 71413 is semiprime and squarefree.
214239 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 142824 totatives.
214239 has a semiprime digit sum 21 in base 10.
214239 has a Fibonacci digit sum 21 in base 10.
214239 has a triangular digit sum 21 in base 10.
214239 = 1071202 - 1071192 = 357082 - 357052 is the difference of 2 nonnegative squares in 2 ways.
214239 is the difference of 2 positive pentagonal numbers in 1 way.
214239 is not the sum of 3 positive squares.
2142392 = 1511642 + 1518152 is the sum of 2 positive squares in 1 way.
2142392 is the sum of 3 positive squares.
214239 is a divisor of 619541 - 1.
214239 is an emirpimes in (at least) the following bases: 3, 5, 7, 11, 15, 21, 23, 29, 35, 43, 45, 50, 51, 52, 53, 55, 57, 58, 61, 63, 66, 69, 80, 81, 82, 83, 89, 90, 96, and 99.
214239 is palindromic in (at least) the following bases: 91, and -75.

Sunday, October 30, 2016

Number of the day: 936907

Properties of the number 936907:

936907 is the 73969th prime.
936907 has 17 antidivisors and 936906 totatives.
936907 has a semiprime digit sum 34 in base 10.
936907 has a Fibonacci digit sum 34 in base 10.
Reversing the decimal digits of 936907 results in a semiprime.
936907 = 4684542 - 4684532 is the difference of 2 nonnegative squares in 1 way.
936907 is the sum of 2 positive triangular numbers.
936907 is the difference of 2 positive pentagonal numbers in 1 way.
936907 = 772 + 1232 + 9572 is the sum of 3 positive squares.
9369072 is the sum of 3 positive squares.
936907 is a divisor of 13156151 - 1.
936907 is an emirp in (at least) the following bases: 2, 3, 4, 5, 11, 14, 15, 17, 23, 25, 29, 34, 38, 43, 50, 51, 57, 59, 67, 71, 77, 82, 84, 88, 97, 98, and 99.

Saturday, October 29, 2016

Number of the day: 933333

Properties of the number 933333:

933333 = 3 × 311111 is semiprime and squarefree.
933333 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 622220 totatives.
Reversing the decimal digits of 933333 results in a sphenic number.
933333 = 4666672 - 4666662 = 1555572 - 1555542 is the difference of 2 nonnegative squares in 2 ways.
933333 is the sum of 2 positive triangular numbers.
933333 is the difference of 2 positive pentagonal numbers in 1 way.
933333 = 552 + 1122 + 9582 is the sum of 3 positive squares.
9333332 is the sum of 3 positive squares.
933333 is a divisor of 1277530 - 1.
933333 is an emirpimes in (at least) the following bases: 6, 13, 21, 25, 30, 31, 45, 50, 54, 57, 69, 71, 72, 78, 81, 82, 87, 92, 93, 96, and 98.
933333 consists of only the digits '3' and '9'.

Friday, October 28, 2016

Number of the day: 104278

Properties of the number 104278:

104278 = 2 × 17 × 3067 is a sphenic number and squarefree.
104278 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 49056 totatives.
104278 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 104278 results in a semiprime.
104278 is the sum of 2 positive triangular numbers.
104278 is the difference of 2 positive pentagonal numbers in 2 ways.
104278 = 92 + 342 + 3212 is the sum of 3 positive squares.
1042782 = 490722 + 920102 is the sum of 2 positive squares in 1 way.
1042782 is the sum of 3 positive squares.
104278 is a divisor of 823112 - 1.
104278 = '10' + '4278' is the concatenation of 2 triangular numbers.
104278 is palindromic in (at least) base -61.

The number 104278 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A206138: G.f.: A(x) = Sum_{n>=0} x^(n*(n+1)/2) / Product_{k=1..n} (1-x^k)^k.

Thursday, October 27, 2016

Number of the day: 6994824442

Properties of the number 6994824442:

6994824442 = 2 × 139 × 577 × 43607 is the 6671248391th composite number and is squarefree.
6994824442 has 4 distinct prime factors, 16 divisors, 43 antidivisors and 3466153728 totatives.
6994824442 is the difference of 2 positive pentagonal numbers in 6 ways.
6994824442 = 5312 + 11842 + 836252 is the sum of 3 positive squares.
69948244422 = 5818918082 + 69705789502 is the sum of 2 positive squares in 1 way.
69948244422 is the sum of 3 positive squares.
6994824442 is a divisor of 1667523272 - 1.
6994824442 = '69' + '94824442' is the concatenation of 2 semiprime numbers.

Wednesday, October 19, 2016

Number of the day: 71771

Properties of the number 71771:

71771 = 7 × 10253 is semiprime and squarefree.
71771 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 61512 totatives.
71771 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 71771 results in an emirpimes.
71771 = 358862 - 358852 = 51302 - 51232 is the difference of 2 nonnegative squares in 2 ways.
71771 is the difference of 2 positive pentagonal numbers in 2 ways.
71771 = 112 + 192 + 2672 is the sum of 3 positive squares.
717712 = 246752 + 673962 is the sum of 2 positive squares in 1 way.
717712 is the sum of 3 positive squares.
71771 is a divisor of 193122 - 1.
71771 is an emirpimes in (at least) the following bases: 3, 5, 6, 10, 11, 15, 24, 31, 32, 33, 34, 39, 43, 46, 48, 53, 55, 56, 61, 64, 67, 68, 74, 85, 87, 88, 91, 93, and 94.
71771 is palindromic in (at least) the following bases: 78, and 80.
71771 consists of only the digits '1' and '7'.

The number 71771 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A079465: Numbers n such that the "inventory" A063850 of n is a perfect square.
A107287: a(n) = a(n-1)+a(n-2)-a(n-3)+a(n-5), n>7.

Tuesday, October 18, 2016

Number of the day: 58959

Properties of the number 58959:

58959 = 32 × 6551 is the 53000th composite number and is not squarefree.
58959 has 2 distinct prime factors, 6 divisors, 7 antidivisors and 39300 totatives.
58959 has a triangular digit sum 36 in base 10.
58959 = 294802 - 294792 = 98282 - 98252 = 32802 - 32712 is the difference of 2 nonnegative squares in 3 ways.
58959 is the sum of 2 positive triangular numbers.
58959 is the difference of 2 positive pentagonal numbers in 1 way.
58959 is not the sum of 3 positive squares.
589592 is the sum of 3 positive squares.
58959 is a divisor of 149350 - 1.
58959 = '58' + '959' is the concatenation of 2 semiprime numbers.
58959 is palindromic in (at least) the following bases: 42, and -64.
58959 in base 20 = 777j and consists of only the digits '7' and 'j'.
58959 in base 42 = XHX and consists of only the digits 'H' and 'X'.

The number 58959 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A013111: arctanh(arcsinh(x)+atan(x))=2*x+13/3!*x^3+561/5!*x^5+58959/7!*x^7...
A061294: a(n) = floor( n^Pi ).

Monday, October 17, 2016

Number of the day: 257768

Properties of the number 257768:

257768 = 23 × 7 × 4603 is the 235111th composite number and is not squarefree.
257768 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 110448 totatives.
257768 has a semiprime digit sum 35 in base 10.
257768 = 644432 - 644412 = 322232 - 322192 = 92132 - 91992 = 46172 - 45892 is the difference of 2 nonnegative squares in 4 ways.
257768 = 242 + 342 + 5062 is the sum of 3 positive squares.
2577682 is the sum of 3 positive squares.
257768 is a divisor of 1796 - 1.

Sunday, October 16, 2016

Number of the day: 59395224035284

Properties of the number 59395224035284:

59395224035284 = 22 × 19079 × 778280099 is composite and not squarefree.
59395224035284 has 3 distinct prime factors, 12 divisors, 111 antidivisors and 29696055419288 totatives.
59395224035284 has a prime digit sum 61 in base 10.
Reversing the decimal digits of 59395224035284 results in a semiprime.
59395224035284 = 148488060088222 - 148488060088202 = 7782991782 - 7782610202 is the difference of 2 nonnegative squares in 2 ways.
59395224035284 is the sum of 2 positive triangular numbers.
59395224035284 is the difference of 2 positive pentagonal numbers in 2 ways.
59395224035284 = 120782 + 193282 + 77067962 is the sum of 3 positive squares.
593952240352842 is the sum of 3 positive squares.
59395224035284 is a divisor of 169715402518371 - 1.

Saturday, October 15, 2016

Number of the day: 5557169278842

Properties of the number 5557169278842:

5557169278842 = 2 × 3 × 926194879807 is a sphenic number and squarefree.
5557169278842 has 3 distinct prime factors, 8 divisors, 39 antidivisors and 1852389759612 totatives.
5557169278842 has a semiprime digit sum 69 in base 10.
5557169278842 = 19522 + 57832 + 23573572 is the sum of 3 positive squares.
55571692788422 is the sum of 3 positive squares.
5557169278842 is a divisor of 144722052259043 - 1.
5557169278842 = '555716927' + '8842' is the concatenation of 2 semiprime numbers.

Friday, October 14, 2016

Number of the day: 8082981598

Properties of the number 8082981598:

8082981598 = 2 × 1559 × 2592361 is a sphenic number and squarefree.
8082981598 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 4038896880 totatives.
8082981598 has an emirpimes digit sum 58 in base 10.
8082981598 is the difference of 2 positive pentagonal numbers in 2 ways.
8082981598 = 4392 + 7742 + 899012 is the sum of 3 positive squares.
80829815982 = 50332003202 + 63246728022 is the sum of 2 positive squares in 1 way.
80829815982 is the sum of 3 positive squares.
8082981598 is a divisor of 50370110 - 1.

Thursday, October 13, 2016

Number of the day: 444870976018

Properties of the number 444870976018:

444870976018 = 2 × 7 × 823 × 1453 × 26573 is composite and squarefree.
444870976018 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 190289107008 totatives.
444870976018 has an emirpimes digit sum 58 in base 10.
444870976018 is the difference of 2 positive pentagonal numbers in 12 ways.
444870976018 = 4572 + 38882 + 6669752 is the sum of 3 positive squares.
4448709760182 = 805668936802 + 4375147551182 = 109154358322 + 4447370442902 = 590064664002 + 4409403839822 = 698076961682 + 4393598421102 is the sum of 2 positive squares in 4 ways.
4448709760182 is the sum of 3 positive squares.
444870976018 is a divisor of 9971377948 - 1.

Wednesday, October 12, 2016

Number of the day: 46271

Properties of the number 46271:

46271 and 46273 form a twin prime pair.
46271 has 13 antidivisors and 46270 totatives.
46271 has an oblong digit sum 20 in base 10.
46271 = 231362 - 231352 is the difference of 2 nonnegative squares in 1 way.
46271 is the sum of 2 positive triangular numbers.
46271 is the difference of 2 positive pentagonal numbers in 1 way.
46271 is not the sum of 3 positive squares.
462712 is the sum of 3 positive squares.
46271 is a divisor of 409661 - 1.
46271 is an emirp in (at least) the following bases: 7, 13, 14, 15, 19, 21, 41, 44, 45, 49, 52, 53, 57, 58, 59, 64, 70, 71, 78, 83, 85, 88, 92, and 96.
46271 is palindromic in (at least) the following bases: -55, -56, and -95.
46271 in base 55 = FGG and consists of only the digits 'F' and 'G'.

The number 46271 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A123107: Prime septets of form k, k+2100, k+4200, k+6300, k+8400, k+10500, k+12600.
A154619: Primes of the form (4n^2+4n-5)/5.
A174370: Lesser member p of a twin prime pair (p, p + 2) such that 2p + 3(p + 2) is a perfect square.
A222105: Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,2,2,1
A226692: The first member of a twin prime pair whose sum equals the sums of k consecutive smaller pairs of twin primes, k=3.
A248367: Initial members of prime quadruples (n, n+2, n+36, n+38).

Tuesday, October 11, 2016

Number of the day: 5007

Properties of the number 5007:

5007 = 3 × 1669 is semiprime and squarefree.
5007 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 3336 totatives.
5007 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 5007 results in a sphenic number.
5007 = 25042 - 25032 = 8362 - 8332 is the difference of 2 nonnegative squares in 2 ways.
5007 is the sum of 2 positive triangular numbers.
5007 is the difference of 2 positive pentagonal numbers in 1 way.
5007 is not the sum of 3 positive squares.
50072 = 34202 + 36572 is the sum of 2 positive squares in 1 way.
50072 is the sum of 3 positive squares.
5007 is a divisor of 18894 - 1.
5007 is an emirpimes in (at least) the following bases: 2, 4, 5, 6, 8, 9, 12, 14, 16, 26, 30, 31, 35, 51, 53, 55, 56, 59, 60, 67, 70, 73, 74, 75, 77, 78, 79, 82, 84, 89, 91, and 98.
5007 is palindromic in (at least) the following bases: 36, -55, and -65.
5007 in base 36 = 3v3 and consists of only the digits '3' and 'v'.

The number 5007 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A022864: a(n) = [ a(n-1)/a(1) ] + [ a(n-2)/a(2) ] + ... + [ a(1)/a(n-1) ], for n >= 3.
A056768: Number of partitions of the n-th prime into prime parts.
A083491: Multiples of 3 in which there is no common digit in successive terms.
A090905: Group the natural numbers such that the n-th group product is a multiple of the (n-1)th group product. (1), (2),(3,4), (5,6,7,8),(9,10,11,12,13,14),(15,16,17,18,19,20,21,22,23,24,25,26),... Sequence contains the first term of each group.
A093911: Group the natural numbers so that the n-th group has at least n members and every group product is a multiple of that of the previous group. a(n) is the first member of the n-th group.
A093916: a(2*k-1)=(2*k-1)^2+2-k, a(2*k)=6*k^2+2-k: First column of the triangle A093915.
A209170: Triangle of coefficients of polynomials u(n,x) jointly generated with A209171; see the Formula section.
A217030: Semiprimes p such that next semiprime after p is p + 10.
A219704: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 nXk array
A236543: Number of partitions of n for which (number of occurrences of the least part) = (number of occurrences of greatest part).

Monday, October 10, 2016

Number of the day: 56717

Properties of the number 56717:

56717 = 43 × 1319 is semiprime and squarefree.
56717 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 55356 totatives.
56717 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 56717 results in a sphenic number.
56717 = 283592 - 283582 = 6812 - 6382 is the difference of 2 nonnegative squares in 2 ways.
56717 is the difference of 2 positive pentagonal numbers in 2 ways.
56717 = 32 + 82 + 2382 is the sum of 3 positive squares.
567172 is the sum of 3 positive squares.
56717 is a divisor of 431659 - 1.
56717 is an emirpimes in (at least) the following bases: 2, 3, 5, 6, 7, 8, 9, 20, 23, 26, 27, 29, 31, 35, 38, 39, 41, 44, 45, 49, 50, 51, 54, 55, 57, 58, 59, 61, 63, 65, 71, 76, 78, 79, 83, 86, 88, 89, 92, 95, and 98.
56717 is palindromic in (at least) the following bases: 64, -15, and -49.
56717 in base 16 = dd8d and consists of only the digits '8' and 'd'.
56717 in base 39 = bBB and consists of only the digits 'B' and 'b'.
56717 in base 48 = OTT and consists of only the digits 'O' and 'T'.

The number 56717 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000690: Landau's approximation to population of x^2 + y^2.
A274974: Centered octahemioctahedral numbers: a(n) = (4*n^3+24*n^2+8*n+3)/3.

Sunday, October 9, 2016

Number of the day: 59378

Properties of the number 59378:

59378 = 2 × 11 × 2699 is a sphenic number and squarefree.
59378 has 3 distinct prime factors, 8 divisors, 49 antidivisors and 26980 totatives.
59378 is the difference of 2 positive pentagonal numbers in 2 ways.
59378 = 12 + 362 + 2412 is the sum of 3 positive squares.
593782 is the sum of 3 positive squares.
59378 is a divisor of 4338 - 1.
59378 is palindromic in (at least) the following bases: 56, and -77.
59378 in base 56 = IqI and consists of only the digits 'I' and 'q'.

The number 59378 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A102296: (1/6)(n+1)(10n^2+17n+12).
A122182: Least positive number k such that 2^k mod k = 2n, or 0 if no such k exists.

Saturday, October 8, 2016

Number of the day: 3176

Properties of the number 3176:

3176 = 23 × 397 is the 2726th composite number and is not squarefree.
3176 has 2 distinct prime factors, 8 divisors, 7 antidivisors and 1584 totatives.
3176 has an emirp digit sum 17 in base 10.
3176 = 243 - 223 is the difference of 2 positive cubes in 1 way.
3176 = 7952 - 7932 = 3992 - 3952 is the difference of 2 nonnegative squares in 2 ways.
3176 = 262 + 502 is the sum of 2 positive squares in 1 way.
3176 = 162 + 342 + 422 is the sum of 3 positive squares.
31762 = 18242 + 26002 is the sum of 2 positive squares in 1 way.
31762 is the sum of 3 positive squares.
3176 is a divisor of 15533 - 1.
3176 is palindromic in (at least) the following bases: 26, and -46.
3176 in base 26 = 4i4 and consists of only the digits '4' and 'i'.
3176 in base 32 = 338 and consists of only the digits '3' and '8'.

The number 3176 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005011: Shifts one place left under 5th order binomial transform.
A005897: a(n) = 6*n^2+2 for n>0, a(0)=1.
A115882: Numbers n such that n plus the n-th prime gives a triangular number.
A139698: Binomial transform of [1, 25, 25, 25,...].
A179202: Numbers n such that phi(n) = phi(n+8), with Euler's totient function phi=A000010.
A192476: Monotonic ordering of set S generated by these rules: if x and y are in S then x^2 + y^2 is in S, and 1 is in S.
A192760: Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
A194434: D-toothpick sequence of the second kind starting with a X-shaped cross formed by 4 D-toothpicks.
A218153: G.f.: A(x) = exp( Sum_{n>=1} x^n/n * Product_{k>=1} (1 + x^(n*k)) ).
A243980: Four times the sum of all divisors of all positive integers <= n.

Friday, October 7, 2016

Number of the day: 394123

Properties of the number 394123:

394123 is the 33408th prime.
394123 has 7 antidivisors and 394122 totatives.
394123 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 394123 results in a semiprime.
394123 = 1970622 - 1970612 is the difference of 2 nonnegative squares in 1 way.
394123 is the sum of 2 positive triangular numbers.
394123 is the difference of 2 positive pentagonal numbers in 1 way.
394123 = 612 + 692 + 6212 is the sum of 3 positive squares.
3941232 is the sum of 3 positive squares.
394123 is a divisor of 3765687 - 1.
394123 = '394' + '123' is the concatenation of 2 emirpimes.
394123 is an emirp in (at least) the following bases: 7, 8, 15, 21, 22, 31, 43, 57, 64, 68, 70, 71, 74, 79, 91, 97, and 100.
394123 is palindromic in (at least) base -96.

The number 394123 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A048361: a(n) is base of smallest triangle containing exactly n 6's.
A119173: Numbers n such that the n-th triangular number contains only digits {2,6,7}.

Thursday, October 6, 2016

Number of the day: 90220

Richard Dedekind was born on this day 185 years ago.

Properties of the number 90220:

90220 = 22 × 5 × 13 × 347 is the 81481th composite number and is not squarefree.
90220 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 33216 totatives.
90220 has an emirp digit sum 13 in base 10.
90220 has a Fibonacci digit sum 13 in base 10.
90220 = 225562 - 225542 = 45162 - 45062 = 17482 - 17222 = 4122 - 2822 is the difference of 2 nonnegative squares in 4 ways.
90220 is the sum of 2 positive triangular numbers.
90220 is the difference of 2 positive pentagonal numbers in 3 ways.
90220 = 342 + 1502 + 2582 is the sum of 3 positive squares.
902202 = 541322 + 721762 = 222082 + 874442 = 458042 + 777282 = 347002 + 832802 is the sum of 2 positive squares in 4 ways.
902202 is the sum of 3 positive squares.
90220 is a divisor of 79346 - 1.
90220 is palindromic in (at least) the following bases: 3, 93, and -97.

Wednesday, October 5, 2016

Number of the day: 4675

Properties of the number 4675:

4675 = 52 × 11 × 17 is the 4042th composite number and is not squarefree.
4675 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 3200 totatives.
4675 has a semiprime digit sum 22 in base 10.
4675 = 23382 - 23372 = 4702 - 4652 = 2182 - 2072 = 1462 - 1292 = 1062 - 812 = 702 - 152 is the difference of 2 nonnegative squares in 6 ways.
4675 is the sum of 2 positive triangular numbers.
4675 is the difference of 2 positive pentagonal numbers in 6 ways.
4675 = 92 + 252 + 632 is the sum of 3 positive squares.
46752 = 22002 + 41252 = 7152 + 46202 = 19802 + 42352 = 32672 + 33442 = 9572 + 45762 = 28052 + 37402 = 13092 + 44882 is the sum of 2 positive squares in 7 ways.
46752 is the sum of 3 positive squares.
4675 is a divisor of 3074 - 1.
4675 = '467' + '5' is the concatenation of 2 prime numbers.
4675 is palindromic in (at least) the following bases: 57, 84, -29, and -82.
4675 in base 30 = 55p and consists of only the digits '5' and 'p'.
4675 in base 56 = 1RR and consists of only the digits '1' and 'R'.
4675 in base 57 = 1P1 and consists of only the digits '1' and 'P'.

The number 4675 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A051798: a(n) = (n+1)*(n+2)*(n+3)*(9n+4)/24.
A091635: Number of primes less than 10^n which do not contain the digit 1.
A129995: a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)*(n^4 + 4)/4!.
A143127: Sum of k*d(k) over k=1,2,...,n, where d(k) is the number of divisors of k.
A157405: A partition product of Stirling_2 type [parameter k = 5] with biggest-part statistic (triangle read by rows).
A216995: Multiples of 11 such that the digit sum is a multiple of 11.
A217088: Numbers n such that (n^89-1)/(n-1) is prime.
A217844: Numbers which are the sums of consecutive fourth powers.
A228413: Count of the first 10^n primes which do not contain the digit 1.
A237823: Number of partitions of n such that (greatest part) + (least part) <= number of parts.

Tuesday, October 4, 2016

Number of the day: 5238697866367

Properties of the number 5238697866367:

5238697866367 = 7 × 149 × 5022720869 is a sphenic number and squarefree.
5238697866367 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 4460176130784 totatives.
5238697866367 = 26193489331842 - 26193489331832 = 3741927047442 - 3741927047372 = 175795231162 - 175795229672 = 25113609562 - 25113599132 is the difference of 2 nonnegative squares in 4 ways.
5238697866367 is the difference of 2 positive pentagonal numbers in 4 ways.
5238697866367 is not the sum of 3 positive squares.
52386978663672 = 24884818817672 + 46099255155802 = 7602769272002 + 51832358936332 = 34797113839672 + 39160648640402 = 17931113502332 + 49222664516202 is the sum of 2 positive squares in 4 ways.
52386978663672 is the sum of 3 positive squares.
5238697866367 is a divisor of 4915022720868 - 1.

Monday, October 3, 2016

Number of the day: 6090

Properties of the number 6090:

6090 = 2 × 3 × 5 × 7 × 29 is the 5295th composite number and is squarefree.
6090 has 5 distinct prime factors, 32 divisors, 19 antidivisors and 1344 totatives.
6090 has an emirpimes digit sum 15 in base 10.
6090 has a triangular digit sum 15 in base 10.
6090 = (14 × 15)/2 + … + (33 × 34)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6090 is the sum of 2 positive triangular numbers.
6090 is the difference of 2 positive pentagonal numbers in 2 ways.
6090 = 192 + 202 + 732 is the sum of 3 positive squares.
60902 = 42002 + 44102 = 7142 + 60482 = 10082 + 60062 = 36542 + 48722 is the sum of 2 positive squares in 4 ways.
60902 is the sum of 3 positive squares.
6090 is a divisor of 3492 - 1.
6090 is palindromic in (at least) base 86.
6090 in base 12 = 3636 and consists of only the digits '3' and '6'.
6090 in base 17 = 1414 and consists of only the digits '1' and '4'.
6090 in base 19 = gga and consists of only the digits 'a' and 'g'.
6090 in base 22 = cci and consists of only the digits 'c' and 'i'.
6090 in base 23 = bbi and consists of only the digits 'b' and 'i'.
6090 in base 29 = 770 and consists of only the digits '0' and '7'.

The number 6090 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024365: Areas of right triangles with co-prime integer sides.
A024406: Ordered areas of primitive Pythagorean triangles.
A046387: Products of 5 distinct primes.
A049385: Triangle of numbers related to triangle A049375; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297...
A051270: Numbers that are divisible by exactly 5 different primes.
A105122: Positive integers n such that n^11 + 1 is semiprime.
A125015: Numbers n for which nontrivial positive magic squares of exactly 8 different orders with magic sum n exist. For a definition of nontrivial positive magic squares, see A125005.
A196837: Coefficient table of numerator polynomials of o.g.f.s for partial sums of powers of positive integers.
A201598: Record (maximal) gaps between prime triplets (p, p+2, p+6).
A242027: Number T(n,k) of endofunctions on [n] with cycles of k distinct lengths; triangle T(n,k), n>=0, 0<=k<=A003056(n), read by rows.

Sunday, October 2, 2016

Number of the day: 7962578852414

Properties of the number 7962578852414:

7962578852414 = 2 × 29 × 53 × 6917 × 374483 is composite and squarefree.
7962578852414 has 5 distinct prime factors, 32 divisors, 31 antidivisors and 3770919897472 totatives.
Reversing the decimal digits of 7962578852414 results in a semiprime.
7962578852414 is the difference of 2 positive pentagonal numbers in 8 ways.
7962578852414 = 6222 + 53732 + 28217992 is the sum of 3 positive squares.
79625788524142 = 47289683281362 + 64062095292302 = 29409116156142 + 73995743695202 = 6307492065602 + 79375573962862 = 53128869376142 + 59309269401202 = 13776218465902 + 78425008784642 = 29735290849142 + 73865273818002 = 50174280892402 + 61828858432142 = 9936501963362 + 79003367819502 = 33300975671602 + 72327803902862 = 54914336913202 + 57660053758862 = 19945301614702 + 77087295591362 = 16163465204642 + 77967997221102 = 42066454314642 + 67606801577102 is the sum of 2 positive squares in 13 ways.
79625788524142 is the sum of 3 positive squares.
7962578852414 is a divisor of 1049390754 - 1.

Saturday, October 1, 2016

Number of the day: 795295

Properties of the number 795295:

795295 = 5 × 159059 is semiprime and squarefree.
795295 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 636232 totatives.
795295 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 795295 results in a prime.
795295 = 3976482 - 3976472 = 795322 - 795272 is the difference of 2 nonnegative squares in 2 ways.
795295 is the sum of 2 positive triangular numbers.
795295 is the difference of 2 positive pentagonal numbers in 2 ways.
795295 is not the sum of 3 positive squares.
7952952 = 4771772 + 6362362 is the sum of 2 positive squares in 1 way.
7952952 is the sum of 3 positive squares.
795295 is a divisor of 9111187 - 1.
795295 is an emirpimes in (at least) the following bases: 3, 5, 8, 18, 23, 25, 30, 33, 50, 53, 54, 55, 59, 62, 67, 71, 76, 77, 82, 85, 87, 91, 92, 93, 95, and 100.