Sunday, July 31, 2016

Number of the day: 93124

Properties of the number 93124:

93124 = 22 × 31 × 751 is the 84129th composite number and is not squarefree.
93124 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 45000 totatives.
93124 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 93124 results in a prime.
93124 = 232822 - 232802 = 7822 - 7202 is the difference of 2 nonnegative squares in 2 ways.
93124 is the sum of 2 positive triangular numbers.
93124 is the difference of 2 positive pentagonal numbers in 2 ways.
93124 = 182 + 1522 + 2642 is the sum of 3 positive squares.
931242 is the sum of 3 positive squares.
93124 is a divisor of 186110 - 1.
93124 in base 7 = 535333 and consists of only the digits '3' and '5'.
93124 in base 49 = ccO and consists of only the digits 'O' and 'c'.

The number 93124 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A179476: Numbers of distinct Knuth-Morris-Pratt arrays of length n.
A245205: Indices of records in A245203 (= least k>=0 such that 4n+3 is the mean of primes 4(n-k)+3 and 4(n+k)+3).

Saturday, July 30, 2016

Number of the day: 74903

Properties of the number 74903:

74903 is the 7388th prime.
74903 has 13 antidivisors and 74902 totatives.
74903 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 74903 results in a semiprime.
74903 = 374522 - 374512 is the difference of 2 nonnegative squares in 1 way.
74903 is the difference of 2 positive pentagonal numbers in 1 way.
74903 is not the sum of 3 positive squares.
749032 is the sum of 3 positive squares.
74903 is a divisor of 592203 - 1.
74903 = '7' + '4903' is the concatenation of 2 prime numbers.
74903 is an emirp in (at least) the following bases: 5, 6, 9, 11, 21, 22, 34, 35, 36, 40, 41, 46, 50, 51, 52, 54, 67, 73, 74, 81, 83, and 95.
74903 is palindromic in (at least) the following bases: 43, 49, and -91.
74903 in base 8 = 222227 and consists of only the digits '2' and '7'.
74903 in base 43 = eLe and consists of only the digits 'L' and 'e'.
74903 in base 49 = V9V and consists of only the digits '9' and 'V'.

The number 74903 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A228771: The number of skew sum indecomposable permutations which avoid the patterns 3124 and 4312.
A240448: Number of partitions p of n such that (sum of parts with multiplicity 1) < (sum of all other parts).

Friday, July 29, 2016

Number of the day: 54250

Properties of the number 54250:

54250 = 2 × 53 × 7 × 31 is the 48731th composite number and is not squarefree.
54250 has 4 distinct prime factors, 32 divisors, 21 antidivisors and 18000 totatives.
54250 is the sum of 2 positive triangular numbers.
54250 is the difference of 2 positive pentagonal numbers in 9 ways.
54250 = 602 + 1392 + 1772 is the sum of 3 positive squares.
542502 = 325502 + 434002 = 151902 + 520802 = 190962 + 507782 is the sum of 2 positive squares in 3 ways.
542502 is the sum of 3 positive squares.
54250 is a divisor of 34910 - 1.
54250 is palindromic in (at least) base -73.
54250 in base 15 = 1111a and consists of only the digits '1' and 'a'.

The number 54250 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A062845: When expressed in base 2 and then interpreted in base 3, is a multiple of the original number.
A143878: Number of ways of placing kings with no more than 2 mutual attacks on an n X n chessboard symmetric about main diagonal.
A202310: Number of (n+2)X3 binary arrays avoiding patterns 001 and 100 in rows and columns
A202315: Number of (n+2)X8 binary arrays avoiding patterns 001 and 100 in rows and columns
A202317: T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 100 in rows and columns
A207437: Number of nX3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically
A219033: Numbers n such that n = x + y, sigma_1(n) = sigma_1(x) + sigma_1(y) and sigma_2(n) = sigma_2(x) + sigma_2(y).

Thursday, July 28, 2016

Number of the day: 526216

Properties of the number 526216:

526216 = 23 × 65777 is the 482676th composite number and is not squarefree.
526216 has 2 distinct prime factors, 8 divisors, 23 antidivisors and 263104 totatives.
526216 has a semiprime digit sum 22 in base 10.
526216 = 1315552 - 1315532 = 657792 - 657752 is the difference of 2 nonnegative squares in 2 ways.
526216 is the difference of 2 positive pentagonal numbers in 2 ways.
526216 = 3302 + 6462 is the sum of 2 positive squares in 1 way.
526216 = 562 + 1742 + 7022 is the sum of 3 positive squares.
5262162 = 3084162 + 4263602 is the sum of 2 positive squares in 1 way.
5262162 is the sum of 3 positive squares.
526216 is a divisor of 174111 - 1.
526216 = '52621' + '6' is the concatenation of 2 semiprime numbers.
526216 is palindromic in (at least) base 98.

The number 526216 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A060824: 4-wave sequence beginning with 2s.

Wednesday, July 27, 2016

Number of the day: 411454

Properties of the number 411454:

411454 = 2 × 409 × 503 is a sphenic number and squarefree.
411454 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 204816 totatives.
411454 has a prime digit sum 19 in base 10.
Reversing the decimal digits of 411454 results in a sphenic number.
411454 is the sum of 2 positive triangular numbers.
411454 is the difference of 2 positive pentagonal numbers in 3 ways.
411454 = 872 + 2622 + 5792 is the sum of 3 positive squares.
4114542 = 1207202 + 3933462 is the sum of 2 positive squares in 1 way.
4114542 is the sum of 3 positive squares.
411454 is a divisor of 1637251 - 1.
411454 = '411' + '454' is the concatenation of 2 semiprime numbers.
411454 is palindromic in (at least) base -88.

Tuesday, July 26, 2016

Number of the day: 583834239360487

Properties of the number 583834239360487:

583834239360487 is prime.
583834239360487 has 53 antidivisors and 583834239360486 totatives.
583834239360487 has an emirp digit sum 73 in base 10.
Reversing the decimal digits of 583834239360487 results in a sphenic number.
583834239360487 = 2919171196802442 - 2919171196802432 is the difference of 2 nonnegative squares in 1 way.
583834239360487 is the sum of 2 positive triangular numbers.
583834239360487 is the difference of 2 positive pentagonal numbers in 1 way.
583834239360487 is not the sum of 3 positive squares.
5838342393604872 is the sum of 3 positive squares.
583834239360487 is a divisor of 732435235520027 - 1.
583834239360487 = '583834' + '239360487' is the concatenation of 2 sphenic numbers.
583834239360487 is an emirp in (at least) the following bases: 11, 31, 34, 36, 71, 76, 77, and 95.

Monday, July 25, 2016

Number of the day: 85117407

Properties of the number 85117407:

85117407 = 3 × 29 × 887 × 1103 is the 80167311th composite number and is squarefree.
85117407 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 54676832 totatives.
85117407 has a semiprime digit sum 33 in base 10.
85117407 = 425587042 - 425587032 = 141862362 - 141862332 = 14675562 - 14675272 = 4892242 - 4891372 = 484242 - 475372 = 391362 - 380332 = 173242 - 146632 = 145162 - 112072 is the difference of 2 nonnegative squares in 8 ways.
85117407 is the sum of 2 positive triangular numbers.
85117407 is the difference of 2 positive pentagonal numbers in 4 ways.
85117407 is not the sum of 3 positive squares.
851174072 = 587016602 + 616367432 is the sum of 2 positive squares in 1 way.
851174072 is the sum of 3 positive squares.
85117407 is a divisor of 34925694 - 1.
85117407 = '85' + '117407' is the concatenation of 2 emirpimes.

Sunday, July 24, 2016

Number of the day: 177084

Properties of the number 177084:

177084 = 22 × 32 × 4919 is the 160992th composite number and is not squarefree.
177084 has 3 distinct prime factors, 18 divisors, 9 antidivisors and 59016 totatives.
177084 = 442722 - 442702 = 147602 - 147542 = 49282 - 49102 is the difference of 2 nonnegative squares in 3 ways.
177084 is the difference of 2 positive pentagonal numbers in 1 way.
177084 is not the sum of 3 positive squares.
1770842 is the sum of 3 positive squares.
177084 is a divisor of 4332459 - 1.
177084 in base 3 = 22222220200 and consists of only the digits '0' and '2'.
177084 in base 35 = 44jj and consists of only the digits '4' and 'j'.

The number 177084 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A273574: Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 801", based on the 5-celled von Neumann neighborhood.

Saturday, July 23, 2016

Number of the day: 81122772871962

Properties of the number 81122772871962:

81122772871962 = 2 × 33 × 777277 × 1932739 is composite and not squarefree.
81122772871962 has 4 distinct prime factors, 32 divisors, 111 antidivisors and 27040875510384 totatives.
81122772871962 = 20922 + 40032 + 90068172 is the sum of 3 positive squares.
811227728719622 = 390390239751122 + 711115945926302 is the sum of 2 positive squares in 1 way.
811227728719622 is the sum of 3 positive squares.
81122772871962 is a divisor of 3891508304078 - 1.
81122772871962 = '81122' + '772871962' is the concatenation of 2 sphenic numbers.

Friday, July 22, 2016

Number of the day: 7222016

Happy Casual π Day!

Properties of the number 7222016:

7222016 = 28 × 28211 is the 6731302th composite number and is not squarefree.
7222016 has 2 distinct prime factors, 18 divisors, 17 antidivisors and 3610880 totatives.
7222016 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 7222016 results in a semiprime.
7222016 = 18055052 - 18055032 = 9027542 - 9027502 = 4513802 - 4513722 = 2256962 - 2256802 = 1128602 - 1128282 = 564542 - 563902 = 282752 - 281472 is the difference of 2 nonnegative squares in 7 ways.
7222016 is the sum of 2 positive triangular numbers.
7222016 is the difference of 2 positive pentagonal numbers in 1 way.
7222016 = 1762 + 6242 + 26082 is the sum of 3 positive squares.
72220162 is the sum of 3 positive squares.
7222016 is a divisor of 593112 - 1.
7222016 = '722201' + '6' is the concatenation of 2 semiprime numbers.

Thursday, July 21, 2016

Number of the day: 248186208075230

Properties of the number 248186208075230:

248186208075230 = 2 × 5 × 829 × 1493 × 4463 × 4493 is composite and squarefree.
248186208075230 has 6 distinct prime factors, 64 divisors, 91 antidivisors and 99044066889216 totatives.
248186208075230 has an oblong digit sum 56 in base 10.
248186208075230 is the difference of 2 positive pentagonal numbers in 14 ways.
248186208075230 = 6582 + 134452 + 157539212 is the sum of 3 positive squares.
2481862080752302 = 1604896970713942 + 1893131031193922 = 390995240573522 + 2450869663961142 = 15453030477262 + 2481813972022322 = 1196994373808242 + 2174130597951182 = 869904926724782 + 2324414938503042 = 507986805510562 + 2429318586209582 = 1238647703836162 + 2150672279464622 = 824973587107022 + 2340738765529362 = 898782324602582 + 2313402196086562 = 1489117248451382 + 1985489664601842 = 536489366551042 + 2423183556285782 = 163461603871022 + 2476473236668642 = 1324546353612482 + 2098860725490862 = 729708522778062 + 2372164593712082 = 362177485335122 + 2455293639667662 = 1364726268106322 + 2072959623585742 = 683883496330542 + 2385779275482722 = 1035172605028662 + 2255672198187122 = 1447381497970962 + 2016116610518222 = 586913557432622 + 2411466745360162 = 215078416714242 + 2472525159131822 = 1368034638146262 + 2070777780619682 = 680073002908082 + 2386868261675062 = 310888074958542 + 2462313544763282 = 1485944912436642 + 1987864961479982 = 540358031429582 + 2422323798699442 = 1167876537428822 + 2189909537218242 = 1051201707317302 + 2248246952274002 = 1021107854076002 + 2262073857817302 = 698725021722002 + 2381474906837302 = 1726098586824802 + 1783317990835502 = 148038957854802 + 2477443007383502 = 1501450807595202 + 1976179359331502 = 1311452362107702 + 2107067177334002 = 744464389632002 + 2367575164687702 = 977349201270002 + 2281321530747702 = 1183434195532502 + 2181541402935202 = 884360768225202 + 2318953518184502 = 839531938004802 + 2335556788636502 = 1616653225098002 + 1883101627012302 is the sum of 2 positive squares in 40 ways.
2481862080752302 is the sum of 3 positive squares.
248186208075230 is a divisor of 106130064956 - 1.

Wednesday, July 20, 2016

Number of the day: 28920

Properties of the number 28920:

28920 = 23 × 3 × 5 × 241 is the 25772th composite number and is not squarefree.
28920 has 4 distinct prime factors, 32 divisors, 9 antidivisors and 7680 totatives.
28920 has a semiprime digit sum 21 in base 10.
28920 has a Fibonacci digit sum 21 in base 10.
28920 has a triangular digit sum 21 in base 10.
28920 = (81 × 82)/2 + … + (88 × 89)/2 = (71 × 72)/2 + … + (80 × 81)/2 is the sum of at least 2 consecutive triangular numbers in 2 ways.
28920 = 72312 - 72292 = 36172 - 36132 = 24132 - 24072 = 14512 - 14412 = 12112 - 11992 = 7332 - 7132 = 4972 - 4672 = 2712 - 2112 is the difference of 2 nonnegative squares in 8 ways.
28920 = (240 × 241)/2 is a triangular number.
28920 is the difference of 2 positive pentagonal numbers in 2 ways.
28920 = 22 + 42 + 1702 is the sum of 3 positive squares.
289202 = 144002 + 250802 = 35282 + 287042 = 114242 + 265682 = 173522 + 231362 is the sum of 2 positive squares in 4 ways.
289202 is the sum of 3 positive squares.
28920 is a divisor of 6594 - 1.
28920 is palindromic in (at least) base 14.
28920 in base 14 = a77a and consists of only the digits '7' and 'a'.
28920 in base 15 = 8880 and consists of only the digits '0' and '8'.
28920 in base 19 = 4422 and consists of only the digits '2' and '4'.
28920 in base 42 = GGO and consists of only the digits 'G' and 'O'.

The number 28920 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000385: Convolution of A000203 with itself.
A068131: Triangular numbers with sum of digits = 21.
A082036: (9*n^2+3*n+1)*n!.
A082038: A square array of quadratic-factorial numbers, read by antidiagonals.
A110450: a(n) = n*(n+1)*(n^2+n+1)/2.
A124494: Numbers n for which 2n-1, 4n-1, 8n-1 and 16n-1 are primes.
A222716: Numbers which are both the sum of n+1 consecutive triangular numbers and the sum of the n-1 immediately following triangular numbers.
A253651: Triangular numbers that are the product of a triangular number and a prime number.
A257712: Triangular numbers (A000217) that are the sum of eight consecutive triangular numbers.
A257713: Triangular numbers (A000217) that are the sum of ten consecutive triangular numbers.

Tuesday, July 19, 2016

Number of the day: 68984

Properties of the number 68984:

68984 = 23 × 8623 is the 62130th composite number and is not squarefree.
68984 has 2 distinct prime factors, 8 divisors, 5 antidivisors and 34488 totatives.
68984 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 68984 results in a sphenic number.
68984 = 582 + … + 732 is the sum of at least 2 consecutive positive squares in 1 way.
68984 = 172472 - 172452 = 86252 - 86212 is the difference of 2 nonnegative squares in 2 ways.
68984 = 422 + 522 + 2542 is the sum of 3 positive squares.
689842 is the sum of 3 positive squares.
68984 is a divisor of 449479 - 1.
68984 = '6898' + '4' is the concatenation of 2 semiprime numbers.
68984 is palindromic in (at least) the following bases: -44, -83, and -89.
68984 in base 51 = QQW and consists of only the digits 'Q' and 'W'.

The number 68984 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A054236: Consider all integer triples (i,j,k), j,k>0, with i^3=j^3+binomial(k+2,3), ordered by increasing i; sequence gives k values.

Monday, July 18, 2016

Number of the day: 337

Properties of the number 337:

337 is the 68th prime.
337 has 11 antidivisors and 336 totatives.
337 has an emirp digit sum 13 in base 10.
337 has a Fibonacci digit sum 13 in base 10.
Reversing the decimal digits of 337 results in an emirp.
337 = 1692 - 1682 is the difference of 2 nonnegative squares in 1 way.
337 is the difference of 2 positive pentagonal numbers in 1 way.
337 = 92 + 162 is the sum of 2 positive squares in 1 way.
337 = 22 + 32 + 182 is the sum of 3 positive squares.
3372 = 1752 + 2882 is the sum of 2 positive squares in 1 way.
3372 is the sum of 3 positive squares.
337 is a divisor of 6732 - 1.
337 = '3' + '37' is the concatenation of 2 prime numbers.
337 is an emirp in (at least) the following bases: 2, 4, 5, 6, 7, 10, 11, 19, 21, 23, 25, 33, 34, 37, 39, 44, 45, 47, 49, 53, 57, 58, 64, 66, 67, 71, 77, 79, 83, 88, 91, 95, and 98.
337 is palindromic in (at least) the following bases: 9, 14, 16, -21, -24, -28, -42, -48, -56, and -84.
337 in base 3 = 110111 and consists of only the digits '0' and '1'.
337 in base 4 = 11101 and consists of only the digits '0' and '1'.
337 in base 5 = 2322 and consists of only the digits '2' and '3'.
337 in base 7 = 661 and consists of only the digits '1' and '6'.
337 in base 9 = 414 and consists of only the digits '1' and '4'.
337 consists of only the digits '3' and '7'.
337 in base 13 = 1cc and consists of only the digits '1' and 'c'.
337 in base 14 = 1a1 and consists of only the digits '1' and 'a'.
337 in base 15 = 177 and consists of only the digits '1' and '7'.
337 in base 16 = 151 and consists of only the digits '1' and '5'.

The number 337 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000695: Moser-de Bruijn sequence: sums of distinct powers of 4.
A002144: Pythagorean primes: primes of form 4n + 1.
A002313: Primes congruent to 1 or 2 modulo 4; or, primes of form x^2+y^2; or, -1 is a square mod p.
A002476: Primes of form 6m + 1.
A005836: Numbers n whose base 3 representation contains no 2.
A006567: Emirps (primes whose reversal is a different prime).
A029495: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 2 (most significant digit on right).
A068228: Primes congruent to 1 (mod 12).
A106856: Primes of the form x^2+xy+2y^2, with x and y nonnegative.
A211422: Number of ordered triples (w,x,y) with all terms in {-n,...,0,...,n} and w^2+x*y=0.

Sunday, July 17, 2016

Number of the day: 7172016

Happy Yellow Pig Day!

Properties of the number 7172016:

7172016 = 24 × 3 × 149417 is the 6684444th composite number and is not squarefree.
7172016 has 3 distinct prime factors, 20 divisors, 11 antidivisors and 2390656 totatives.
Reversing the decimal digits of 7172016 results in a semiprime.
7172016 = 17930052 - 17930032 = 8965042 - 8965002 = 5976712 - 5976652 = 4482552 - 4482472 = 2988402 - 2988282 = 1494292 - 1494052 is the difference of 2 nonnegative squares in 6 ways.
7172016 is the difference of 2 positive pentagonal numbers in 1 way.
7172016 = 3802 + 4042 + 26202 is the sum of 3 positive squares.
71720162 = 27651842 + 66175202 is the sum of 2 positive squares in 1 way.
71720162 is the sum of 3 positive squares.
7172016 is a divisor of 14478 - 1.
7172016 is palindromic in (at least) base -79.

Saturday, July 16, 2016

Number of the day: 47455

Properties of the number 47455:

47455 = 5 × 9491 is semiprime and squarefree.
47455 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 37960 totatives.
47455 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 47455 results in an emirpimes.
47455 = 237282 - 237272 = 47482 - 47432 is the difference of 2 nonnegative squares in 2 ways.
47455 is the difference of 2 positive pentagonal numbers in 2 ways.
47455 is not the sum of 3 positive squares.
474552 = 284732 + 379642 is the sum of 2 positive squares in 1 way.
474552 is the sum of 3 positive squares.
47455 is a divisor of 155352 - 1.
47455 is an emirpimes in (at least) the following bases: 3, 9, 10, 12, 15, 17, 20, 21, 27, 28, 30, 32, 34, 35, 41, 43, 49, 57, 67, 68, 73, 75, 80, 83, 90, 92, and 94.
47455 is palindromic in (at least) the following bases: 39, and -43.
47455 in base 38 = WWV and consists of only the digits 'V' and 'W'.
47455 in base 39 = V7V and consists of only the digits '7' and 'V'.
47455 in base 42 = Qbb and consists of only the digits 'Q' and 'b'.

The number 47455 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A184629: Floor(1/{(5+n^4)^(1/4)}), where {}=fractional part.

Friday, July 15, 2016

Number of the day: 71747223424938

Properties of the number 71747223424938:

71747223424938 = 2 × 33 × 1328652285647 is composite and not squarefree.
71747223424938 has 3 distinct prime factors, 16 divisors, 83 antidivisors and 23915741141628 totatives.
71747223424938 is the difference of 2 positive pentagonal numbers in 2 ways.
71747223424938 = 89802 + 139672 + 84703572 is the sum of 3 positive squares.
717472234249382 is the sum of 3 positive squares.
71747223424938 is a divisor of 811189807469378 - 1.
71747223424938 = '717472234' + '24938' is the concatenation of 2 sphenic numbers.

Thursday, July 14, 2016

Number of the day: 7978734663674

Properties of the number 7978734663674:

7978734663674 = 2 × 29 × 137564390753 is a sphenic number and squarefree.
7978734663674 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 3851802941056 totatives.
7978734663674 has a semiprime digit sum 77 in base 10.
Reversing the decimal digits of 7978734663674 results in a sphenic number.
7978734663674 is the difference of 2 positive pentagonal numbers in 2 ways.
7978734663674 = 19331752 + 20595072 = 1581432 + 28202352 is the sum of 2 positive squares in 2 ways.
7978734663674 = 56272 + 78122 + 28246492 is the sum of 3 positive squares.
79787346636742 = 51263111806242 + 61140118181702 = 8920008472102 + 79287162467762 = 5044035024242 + 79627748894502 = 55025756301202 + 57777044116262 is the sum of 2 positive squares in 4 ways.
79787346636742 is the sum of 3 positive squares.
7978734663674 is a divisor of 7432494691024 - 1.

Wednesday, July 13, 2016

Number of the day: 814913

Properties of the number 814913:

814913 = 11 × 23 × 3221 is a sphenic number and squarefree.
814913 has 3 distinct prime factors, 8 divisors, 31 antidivisors and 708400 totatives.
814913 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 814913 results in a sphenic number.
814913 = 4074572 - 4074562 = 370472 - 370362 = 177272 - 177042 = 17372 - 14842 is the difference of 2 nonnegative squares in 4 ways.
814913 is the difference of 2 positive pentagonal numbers in 4 ways.
814913 = 712 + 842 + 8962 is the sum of 3 positive squares.
8149132 = 3896202 + 7157372 is the sum of 2 positive squares in 1 way.
8149132 is the sum of 3 positive squares.
814913 is a divisor of 647220 - 1.

Tuesday, July 12, 2016

Number of the day: 175286

Properties of the number 175286:

175286 = 2 × 87643 is semiprime and squarefree.
175286 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 87642 totatives.
175286 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 175286 results in a sphenic number.
175286 is the sum of 2 positive triangular numbers.
175286 = 62 + 552 + 4152 is the sum of 3 positive squares.
1752862 is the sum of 3 positive squares.
175286 is a divisor of 145381 - 1.
175286 is an emirpimes in (at least) the following bases: 4, 5, 14, 18, 23, 25, 26, 28, 32, 35, 36, 44, 46, 48, 49, 50, 52, 56, 61, 62, 64, 67, 71, 78, 80, 81, 97, and 99.
175286 is palindromic in (at least) base 76.
175286 in base 25 = b5bb and consists of only the digits '5' and 'b'.

The number 175286 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A257441: Number of (n+2)X(2+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 3 and no row sum 1 and no column sum 1

Monday, July 11, 2016

Number of the day: 47435

Properties of the number 47435:

47435 = 5 × 53 × 179 is a sphenic number and squarefree.
47435 has 3 distinct prime factors, 8 divisors, 19 antidivisors and 37024 totatives.
47435 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 47435 results in a semiprime.
47435 = 237182 - 237172 = 47462 - 47412 = 4742 - 4212 = 2222 - 432 is the difference of 2 nonnegative squares in 4 ways.
47435 is the difference of 2 positive pentagonal numbers in 3 ways.
47435 = 112 + 152 + 2172 is the sum of 3 positive squares.
474352 = 284612 + 379482 = 171842 + 442132 = 41172 + 472562 = 250602 + 402752 is the sum of 2 positive squares in 4 ways.
474352 is the sum of 3 positive squares.
47435 is a divisor of 178926 - 1.
47435 = '4' + '7435' is the concatenation of 2 semiprime numbers.
47435 is palindromic in (at least) the following bases: 64, 90, and 93.
47435 in base 38 = WWB and consists of only the digits 'B' and 'W'.

The number 47435 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A034081: Decimal part of n-th root of a(n) starts with digit 4.
A204657: Numbers n such that n!10+2 is prime.
A244834: Number of length 3 0..n arrays with each partial sum starting from the beginning no more than two standard deviataions from its mean

Sunday, July 10, 2016

Number of the day: 9488

Properties of the number 9488:

9488 = 24 × 593 is the 8312th composite number and is not squarefree.
9488 has 2 distinct prime factors, 10 divisors, 25 antidivisors and 4736 totatives.
9488 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 9488 results in a prime.
9488 = 23732 - 23712 = 11882 - 11842 = 5972 - 5892 is the difference of 2 nonnegative squares in 3 ways.
9488 is the sum of 2 positive triangular numbers.
9488 is the difference of 2 positive pentagonal numbers in 1 way.
9488 = 322 + 922 is the sum of 2 positive squares in 1 way.
9488 = 42 + 162 + 962 is the sum of 3 positive squares.
94882 = 58882 + 74402 is the sum of 2 positive squares in 1 way.
94882 is the sum of 3 positive squares.
9488 is a divisor of 11094 - 1.
9488 is palindromic in (at least) the following bases: 62, and -93.
9488 in base 43 = 55S and consists of only the digits '5' and 'S'.
9488 in base 61 = 2XX and consists of only the digits '2' and 'X'.
9488 in base 62 = 2T2 and consists of only the digits '2' and 'T'.

The number 9488 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001672: Floor(Pi^n).
A058498: Number of solutions to c(1)t(1)+...+c(n)t(n) = 0, where c(i) = +-1 for i>1, c(1) = t(1) = 1, t(i) = triangular numbers (A000217).
A085150: Numbers n such that n!!!!!!+1 is prime.
A112861: Numbers n such that (2*n)!/(2*(n!)^2) - 1 is prime.
A163832: n*(2*n^2+5*n+1).
A226490: a(n) = n*(19*n-15)/2.
A231285: T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero
A240675: Number of partitions p of n such that exactly one number is in both p and its conjugate.
A265067: Coordination sequence for (2,5,8) tiling of hyperbolic plane.
A268037: Numbers n such that the number of divisors of n+2 divides n and the number of divisors of n divides n+2.

Saturday, July 9, 2016

Number of the day: 25337470925392

Properties of the number 25337470925392:

25337470925392 = 24 × 357569 × 4428773 is composite and not squarefree.
25337470925392 has 3 distinct prime factors, 20 divisors, 79 antidivisors and 12668697171968 totatives.
25337470925392 has a prime digit sum 61 in base 10.
25337470925392 = 63343677313492 - 63343677313472 = 31671838656762 - 31671838656722 = 15835919328412 - 15835919328332 = 180726612 - 173575232 = 95726842 - 81424082 = 58590492 - 29984972 is the difference of 2 nonnegative squares in 6 ways.
25337470925392 is the difference of 2 positive pentagonal numbers in 1 way.
25337470925392 = 15926162 + 47750442 = 8183642 + 49666642 is the sum of 2 positive squares in 2 ways.
25337470925392 = 30362 + 337362 + 50335202 is the sum of 3 positive squares.
253374709253922 = 81290780353922 + 239980316524002 = 40022644450082 + 250193787334402 = 152096229502082 + 202646194784802 = 118177126610402 + 224126995329922 is the sum of 2 positive squares in 4 ways.
253374709253922 is the sum of 3 positive squares.
25337470925392 is a divisor of 641629406656 - 1.

Friday, July 8, 2016

Number of the day: 3088281

Properties of the number 3088281:

3088281 = 3 × 7 × 199 × 739 is the 2865567th composite number and is squarefree.
3088281 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 1753488 totatives.
3088281 has a sphenic digit sum 30 in base 10.
3088281 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 3088281 results in a semiprime.
3088281 = 15441412 - 15441402 = 5147152 - 5147122 = 2205952 - 2205882 = 735412 - 735202 = 78592 - 76602 = 28852 - 22882 = 24592 - 17202 = 18052 - 4122 is the difference of 2 nonnegative squares in 8 ways.
3088281 is the difference of 2 positive pentagonal numbers in 3 ways.
3088281 = 892 + 2142 + 17422 is the sum of 3 positive squares.
30882812 is the sum of 3 positive squares.
3088281 is a divisor of 41918 - 1.

Thursday, July 7, 2016

Number of the day: 598076

Properties of the number 598076:

598076 = 22 × 149519 is the 549118th composite number and is not squarefree.
598076 has 2 distinct prime factors, 6 divisors, 21 antidivisors and 299036 totatives.
598076 has a semiprime digit sum 35 in base 10.
Reversing the decimal digits of 598076 results in a sphenic number.
598076 = 1495202 - 1495182 is the difference of 2 nonnegative squares in 1 way.
598076 is the difference of 2 positive pentagonal numbers in 1 way.
598076 is not the sum of 3 positive squares.
5980762 is the sum of 3 positive squares.
598076 is a divisor of 574759 - 1.
598076 = '59807' + '6' is the concatenation of 2 semiprime numbers.

Wednesday, July 6, 2016

Number of the day: 688

Properties of the number 688:

688 = 24 × 43 is the 563th composite number and is not squarefree.
688 has 2 distinct prime factors, 10 divisors, 15 antidivisors and 336 totatives.
688 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 688 results in a semiprime.
688 = 1732 - 1712 = 882 - 842 = 472 - 392 is the difference of 2 nonnegative squares in 3 ways.
688 is the sum of 2 positive triangular numbers.
688 is the difference of 2 positive pentagonal numbers in 1 way.
688 = 122 + 122 + 202 is the sum of 3 positive squares.
6882 is the sum of 3 positive squares.
688 is a divisor of 2572 - 1.
688 is palindromic in (at least) the following bases: 7, 12, 42, 85, and -11.
688 in base 3 = 221111 and consists of only the digits '1' and '2'.
688 in base 7 = 2002 and consists of only the digits '0' and '2'.
688 in base 9 = 844 and consists of only the digits '4' and '8'.
688 consists of only the digits '6' and '8'.
688 in base 12 = 494 and consists of only the digits '4' and '9'.
688 in base 18 = 224 and consists of only the digits '2' and '4'.

The number 688 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001743: Every digit contains at least one loop (version 1).
A006313: Numbers n such that n^16 + 1 is prime.
A008484: Number of partitions of n into parts >= 4.
A008598: Multiples of 16.
A014614: Numbers that are products of 5 primes (or 5-almost primes, a generalization of semiprimes).
A026797: Number of partitions of n in which the least part is 4.
A035607: Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d>=1, m >= 0).
A049600: Array T read by diagonals; T(i,j)=number of paths from (0,0) to (i,j) consisting of nonvertical segments (x(k),y(k))-to-(x(k+1),y(k+1)) such that 0=x(1)<x(2)<...<x(n-1)<x(n)=i, 0=y(1)<=y(2)<=...y(n-1)<=y(n)=j, for i >= 0, j >= 0.
A121028: Multiples of 8 containing a 8 in their decimal representation.
A178739: Product of the 4th power of a prime (A030514) and a different prime.

Tuesday, July 5, 2016

Number of the day: 5735

Properties of the number 5735:

5735 = 5 × 31 × 37 is a sphenic number and squarefree.
5735 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 4320 totatives.
5735 has an oblong digit sum 20 in base 10.
5735 = 223 - 173 is the difference of 2 positive cubes in 1 way.
5735 = 28682 - 28672 = 5762 - 5712 = 1082 - 772 = 962 - 592 is the difference of 2 nonnegative squares in 4 ways.
5735 is the sum of 2 positive triangular numbers.
5735 is the difference of 2 positive pentagonal numbers in 2 ways.
5735 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
5735 = (62 × (3 × 62-1))/2 is a pentagonal number.
5735 is not the sum of 3 positive squares.
57352 = 18602 + 54252 = 17672 + 54562 = 32242 + 47432 = 34412 + 45882 is the sum of 2 positive squares in 4 ways.
57352 is the sum of 3 positive squares.
5735 is a divisor of 2113 - 1.
5735 = '57' + '35' is the concatenation of 2 semiprime numbers.
5735 is palindromic in (at least) the following bases: 49, 61, -19, -20, -25, -63, and -94.
5735 in base 9 = 7772 and consists of only the digits '2' and '7'.
5735 in base 11 = 4344 and consists of only the digits '3' and '4'.
5735 in base 19 = fgg and consists of only the digits 'f' and 'g'.
5735 in base 48 = 2NN and consists of only the digits '2' and 'N'.
5735 in base 49 = 2J2 and consists of only the digits '2' and 'J'.
5735 in base 53 = 22B and consists of only the digits '2' and 'B'.
5735 in base 60 = 1ZZ and consists of only the digits '1' and 'Z'.
5735 in base 61 = 1X1 and consists of only the digits '1' and 'X'.

The number 5735 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A029552: Expansion of phi(x) / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
A037277: Replace n by concatenation of its divisors >1.
A037284: Replace n by concatenation of its odd divisors >1.
A037285: Replace n by concatenation of its nontrivial odd divisors.
A049452: Pentagonal numbers with even index.
A138990: a(n) = Frobenius number for 4 successive primes = F[p(n),p(n+1),p(n+2),p(n+3)].
A185258: Side of triangle of the difference of pairs of triangular numbers whose sum and difference are triangular.
A202461: T(n,k)=Number of (n+2)X(k+2) binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column
A265065: Coordination sequence for (2,5,6) tiling of hyperbolic plane.
A271926: Denominator of (Prod(((2*j+1)*(3*j+4))/((j+1)*(6*j+1)),j=0..n-1)-1).

Monday, July 4, 2016

Number of the day: 878992766580

Properties of the number 878992766580:

878992766580 = 22 × 3 × 5 × 89 × 163 × 167 × 6047 is composite and not squarefree.
878992766580 has 7 distinct prime factors, 192 divisors, 79 antidivisors and 228925357056 totatives.
878992766580 is the difference of 2 nonnegative squares in 32 ways.
878992766580 is the difference of 2 positive pentagonal numbers in 15 ways.
878992766580 = 45822 + 59602 + 9375162 is the sum of 3 positive squares.
8789927665802 = 5273956599482 + 7031942132642 = 1659222300962 + 8631906494282 = 4009787227322 + 7822047990242 = 3851766055802 + 7901058576002 is the sum of 2 positive squares in 4 ways.
8789927665802 is the sum of 3 positive squares.
878992766580 is a divisor of 16695386986 - 1.

Sunday, July 3, 2016

Number of the day: 8281436537

Properties of the number 8281436537:

8281436537 = 11 × 41 × 113 × 162499 is the 7901318249th composite number and is squarefree.
8281436537 has 4 distinct prime factors, 16 divisors, 27 antidivisors and 7279910400 totatives.
8281436537 has a prime digit sum 47 in base 10.
8281436537 = 41407182692 - 41407182682 = 3764289392 - 3764289282 = 1009931492 - 1009931082 = 366435812 - 366434682 = 91814192 - 91809682 = 33318512 - 33306082 = 8960612 - 8914282 = 1067312 - 557682 is the difference of 2 nonnegative squares in 8 ways.
8281436537 is the sum of 2 positive triangular numbers.
8281436537 is the difference of 2 positive pentagonal numbers in 8 ways.
8281436537 = 582 + 2632 + 910022 is the sum of 3 positive squares.
82814365372 = 18178763132 + 80794502802 = 7292955122 + 82492617352 = 28742823122 + 77666397052 = 10993057352 + 82081494882 is the sum of 2 positive squares in 4 ways.
82814365372 is the sum of 3 positive squares.
8281436537 is a divisor of 14535110 - 1.
8281436537 = '828143' + '6537' is the concatenation of 2 semiprime numbers.
8281436537 = '82814' + '36537' is the concatenation of 2 sphenic numbers.

Saturday, July 2, 2016

Number of the day: 146549

Properties of the number 146549:

146549 = 13 × 11273 is semiprime and squarefree.
146549 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 135264 totatives.
146549 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 146549 results in an emirpimes.
146549 = 732752 - 732742 = 56432 - 56302 is the difference of 2 nonnegative squares in 2 ways.
146549 is the sum of 2 positive triangular numbers.
146549 is the difference of 2 positive pentagonal numbers in 2 ways.
146549 = 1702 + 3432 = 252 + 3822 is the sum of 2 positive squares in 2 ways.
146549 = 522 + 632 + 3742 is the sum of 3 positive squares.
1465492 = 735152 + 1267762 = 191002 + 1452992 = 887492 + 1166202 = 563652 + 1352762 is the sum of 2 positive squares in 4 ways.
1465492 is the sum of 3 positive squares.
146549 is a divisor of 1311409 - 1.
146549 = '1465' + '49' is the concatenation of 2 semiprime numbers.
146549 is an emirpimes in (at least) the following bases: 4, 5, 10, 11, 13, 16, 17, 21, 22, 27, 29, 31, 33, 36, 39, 42, 44, 48, 52, 56, 58, 61, 64, 65, 69, 77, 79, 82, 83, 85, 88, 89, 92, 97, 99, and 100.
146549 is palindromic in (at least) base -72.

The number 146549 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A031618: Numbers n such that continued fraction for sqrt(n) has odd period and central terms 30.

Friday, July 1, 2016

Number of the day: 589773

Gottfried Wilhelm Leibniz was born on this day 370 years ago.

Properties of the number 589773:

589773 = 3 × 29 × 6779 is a sphenic number and squarefree.
589773 has 3 distinct prime factors, 8 divisors, 13 antidivisors and 379568 totatives.
589773 has an emirpimes digit sum 39 in base 10.
589773 = 2948872 - 2948862 = 982972 - 982942 = 101832 - 101542 = 34332 - 33462 is the difference of 2 nonnegative squares in 4 ways.
589773 is the difference of 2 positive pentagonal numbers in 2 ways.
589773 = 372 + 1702 + 7482 is the sum of 3 positive squares.
5897732 = 4067402 + 4270772 is the sum of 2 positive squares in 1 way.
5897732 is the sum of 3 positive squares.
589773 is a divisor of 3493389 - 1.
589773 = '5897' + '73' is the concatenation of 2 prime numbers.
589773 = '58' + '9773' is the concatenation of 2 semiprime numbers.