Friday, September 30, 2016

Number of the day: 454962

Properties of the number 454962:

454962 = 2 × 3 × 191 × 397 is the 416882th composite number and is squarefree.
454962 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 150480 totatives.
454962 has a sphenic digit sum 30 in base 10.
454962 has an oblong digit sum 30 in base 10.
Reversing the decimal digits of 454962 results in a sphenic number.
454962 is the sum of 2 positive triangular numbers.
454962 is the difference of 2 positive pentagonal numbers in 2 ways.
454962 = 252 + 642 + 6712 is the sum of 3 positive squares.
4549622 = 2612882 + 3724502 is the sum of 2 positive squares in 1 way.
4549622 is the sum of 3 positive squares.
454962 is a divisor of 38318 - 1.
454962 = '4' + '54962' is the concatenation of 2 semiprime numbers.

Thursday, September 29, 2016

Number of the day: 29464680473917

Properties of the number 29464680473917:

29464680473917 = 13 × 647 × 3503112647 is a sphenic number and squarefree.
29464680473917 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 27156129231792 totatives.
29464680473917 has a sphenic digit sum 70 in base 10.
29464680473917 = 147323402369592 - 147323402369582 = 11332569413112 - 11332569412982 = 227702325292 - 227702318822 = 17515605292 - 17515521182 is the difference of 2 nonnegative squares in 4 ways.
29464680473917 is the difference of 2 positive pentagonal numbers in 4 ways.
29464680473917 = 78162 + 155312 + 54281102 is the sum of 3 positive squares.
294646804739172 = 113325694130452 + 271981665913082 is the sum of 2 positive squares in 1 way.
294646804739172 is the sum of 3 positive squares.
29464680473917 is a divisor of 13618120852043 - 1.
29464680473917 = '2946468047' + '3917' is the concatenation of 2 prime numbers.

Wednesday, September 28, 2016

Number of the day: 55960

Properties of the number 55960:

55960 = 23 × 5 × 1399 is the 50279th composite number and is not squarefree.
55960 has 3 distinct prime factors, 16 divisors, 5 antidivisors and 22368 totatives.
55960 has a semiprime digit sum 25 in base 10.
55960 = 139912 - 139892 = 69972 - 69932 = 28032 - 27932 = 14092 - 13892 is the difference of 2 nonnegative squares in 4 ways.
55960 is the sum of 2 positive triangular numbers.
55960 is the difference of 2 positive pentagonal numbers in 2 ways.
55960 = 302 + 762 + 2222 is the sum of 3 positive squares.
559602 = 335762 + 447682 is the sum of 2 positive squares in 1 way.
559602 is the sum of 3 positive squares.
55960 is a divisor of 10096 - 1.
55960 is palindromic in (at least) the following bases: -71, and -75.

The number 55960 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A157660: 8000n - 40.

Tuesday, September 27, 2016

Number of the day: 46040

Properties of the number 46040:

46040 = 23 × 5 × 1151 is the 41276th composite number and is not squarefree.
46040 has 3 distinct prime factors, 16 divisors, 17 antidivisors and 18400 totatives.
46040 has a semiprime digit sum 14 in base 10.
46040 = 115112 - 115092 = 57572 - 57532 = 23072 - 22972 = 11612 - 11412 is the difference of 2 nonnegative squares in 4 ways.
46040 is the difference of 2 positive pentagonal numbers in 2 ways.
46040 = 102 + 122 + 2142 is the sum of 3 positive squares.
460402 = 276242 + 368322 is the sum of 2 positive squares in 1 way.
460402 is the sum of 3 positive squares.
46040 is a divisor of 161910 - 1.
46040 is palindromic in (at least) the following bases: 93, -67, and -99.
46040 in base 59 = DDK and consists of only the digits 'D' and 'K'.

The number 46040 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A120543: Bond series for second parallel moment of hexagonal net.
A120549: Site percolation series for Kagome lattice.
A157652: 8000n - 1960.
A224141: Number of nX3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing

Monday, September 26, 2016

Number of the day: 890943

Properties of the number 890943:

890943 = 3 × 296981 is semiprime and squarefree.
890943 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 593960 totatives.
890943 has a semiprime digit sum 33 in base 10.
890943 = 4454722 - 4454712 = 1484922 - 1484892 is the difference of 2 nonnegative squares in 2 ways.
890943 is the difference of 2 positive pentagonal numbers in 1 way.
890943 is not the sum of 3 positive squares.
8909432 = 1176572 + 8831402 is the sum of 2 positive squares in 1 way.
8909432 is the sum of 3 positive squares.
890943 is a divisor of 971310 - 1.
890943 is an emirpimes in (at least) the following bases: 4, 12, 14, 17, 23, 26, 27, 30, 31, 39, 50, 57, 63, 64, 66, 71, 72, 77, 78, 81, 82, 84, 87, 90, and 91.
890943 is palindromic in (at least) base -97.

Sunday, September 25, 2016

Number of the day: 797509

Properties of the number 797509:

797507 and 797509 form a twin prime pair.
797509 has 5 antidivisors and 797508 totatives.
797509 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 797509 results in a semiprime.
797509 = 3987552 - 3987542 is the difference of 2 nonnegative squares in 1 way.
797509 is the difference of 2 positive pentagonal numbers in 1 way.
797509 = 2222 + 8652 is the sum of 2 positive squares in 1 way.
797509 = 822 + 1532 + 8762 is the sum of 3 positive squares.
7975092 = 3840602 + 6989412 is the sum of 2 positive squares in 1 way.
7975092 is the sum of 3 positive squares.
797509 is a divisor of 6122153 - 1.
797509 = '797' + '509' is the concatenation of 2 prime numbers.
797509 is an emirp in (at least) the following bases: 15, 21, 25, 30, 36, 37, 54, 55, 57, 59, 65, 67, 69, 83, 91, 92, and 100.
797509 is palindromic in (at least) base 98.
797509 in base 17 = 99595 and consists of only the digits '5' and '9'.

Saturday, September 24, 2016

Number of the day: 28470

Gerolamo Cardano was born on this day 515 years ago.

Properties of the number 28470:

28470 = 2 × 3 × 5 × 13 × 73 is the 25372th composite number and is squarefree.
28470 has 5 distinct prime factors, 32 divisors, 17 antidivisors and 6912 totatives.
28470 has a semiprime digit sum 21 in base 10.
28470 has a Fibonacci digit sum 21 in base 10.
28470 has a triangular digit sum 21 in base 10.
28470 = (75 × 76)/2 + … + (83 × 84)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
28470 is the difference of 2 positive pentagonal numbers in 3 ways.
28470 = 262 + 352 + 1632 is the sum of 3 positive squares.
284702 = 187202 + 214502 = 90302 + 270002 = 126002 + 255302 = 89762 + 270182 = 21062 + 283922 = 128642 + 253982 = 59282 + 278462 = 52382 + 279842 = 161822 + 234242 = 170822 + 227762 = 70082 + 275942 = 144542 + 245282 = 109502 + 262802 is the sum of 2 positive squares in 13 ways.
284702 is the sum of 3 positive squares.
28470 is a divisor of 14874 - 1.
28470 is palindromic in (at least) the following bases: 41, and -86.
28470 in base 3 = 1110001110 and consists of only the digits '0' and '1'.
28470 in base 27 = 1c1c and consists of only the digits '1' and 'c'.
28470 in base 41 = GcG and consists of only the digits 'G' and 'c'.

The number 28470 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A062254: 3rd level triangle related to Eulerian numbers and binomial transforms (A062253 is second level, triangle of Eulerian numbers is first level and triangle with Z(0,0)=1 and Z(n,k)=0 otherwise is 0th level).
A133409: Zero followed by partial sums of A133405.
A217020: Eulerian numbers of the third order.

Friday, September 23, 2016

Number of the day: 92806737

Properties of the number 92806737:

92806737 = 3 × 283 × 109313 is a sphenic number and squarefree.
92806737 has 3 distinct prime factors, 8 divisors, 17 antidivisors and 61651968 totatives.
92806737 has a sphenic digit sum 42 in base 10.
92806737 has an oblong digit sum 42 in base 10.
Reversing the decimal digits of 92806737 results in a sphenic number.
92806737 = 464033692 - 464033682 = 154677912 - 154677882 = 1641112 - 1638282 = 550812 - 542322 is the difference of 2 nonnegative squares in 4 ways.
92806737 is the sum of 2 positive triangular numbers.
92806737 is the difference of 2 positive pentagonal numbers in 2 ways.
92806737 = 1762 + 4812 + 96202 is the sum of 3 positive squares.
928067372 = 193444652 + 907682882 is the sum of 2 positive squares in 1 way.
928067372 is the sum of 3 positive squares.
92806737 is a divisor of 18475734 - 1.

Thursday, September 22, 2016

Number of the day: 6211547495646

Properties of the number 6211547495646:

6211547495646 = 2 × 3 × 43 × 563 × 42763349 is composite and squarefree.
6211547495646 has 5 distinct prime factors, 32 divisors, 47 antidivisors and 2018772132384 totatives.
Reversing the decimal digits of 6211547495646 results in a sphenic number.
6211547495646 is the difference of 2 positive pentagonal numbers in 4 ways.
6211547495646 = 4992 + 17062 + 24922972 is the sum of 3 positive squares.
62115474956462 = 28176227118542 + 55357316178002 is the sum of 2 positive squares in 1 way.
62115474956462 is the sum of 3 positive squares.
6211547495646 is a divisor of 953783684834 - 1.
6211547495646 = '621154' + '7495646' is the concatenation of 2 semiprime numbers.
6211547495646 = '6211547' + '495646' is the concatenation of 2 sphenic numbers.

Wednesday, September 21, 2016

Number of the day: 25233702813143

Properties of the number 25233702813143:

25233702813143 = 11 × 83 × 122299 × 225989 is composite and squarefree.
25233702813143 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 22663061947680 totatives.
25233702813143 = 126168514065722 - 126168514065712 = 11469864915122 - 11469864915012 = 1520102579522 - 1520102578692 = 138191148122 - 138191138992 = 1032251282 - 1031028292 = 559424882 - 557164992 = 100511882 - 87058992 = 63183482 - 38324692 is the difference of 2 nonnegative squares in 8 ways.
25233702813143 is the difference of 2 positive pentagonal numbers in 7 ways.
25233702813143 is not the sum of 3 positive squares.
252337028131432 = 172736452889002 + 183945898593932 is the sum of 2 positive squares in 1 way.
252337028131432 is the sum of 3 positive squares.
25233702813143 is a divisor of 293818988940 - 1.
25233702813143 = '252337028131' + '43' is the concatenation of 2 prime numbers.
25233702813143 = '25233' + '702813143' is the concatenation of 2 sphenic numbers.

Tuesday, September 20, 2016

Number of the day: 67158866076

Properties of the number 67158866076:

67158866076 = 22 × 3 × 5596572173 is composite and not squarefree.
67158866076 has 3 distinct prime factors, 12 divisors, 7 antidivisors and 22386288688 totatives.
67158866076 = 167897165202 - 167897165182 = 55965721762 - 55965721702 is the difference of 2 nonnegative squares in 2 ways.
67158866076 is the sum of 2 positive triangular numbers.
67158866076 is the difference of 2 positive pentagonal numbers in 1 way.
67158866076 is not the sum of 3 positive squares.
671588660762 = 174909593762 + 648411877802 is the sum of 2 positive squares in 1 way.
671588660762 is the sum of 3 positive squares.
67158866076 is a divisor of 611399143043 - 1.

Monday, September 19, 2016

Number of the day: 4079899757679

Ky Fan was born on this day 102 years ago.

Properties of the number 4079899757679:

4079899757679 = 3 × 89 × 409 × 2549 × 14657 is composite and squarefree.
4079899757679 has 5 distinct prime factors, 32 divisors, 43 antidivisors and 2681561186304 totatives.
4079899757679 has a semiprime digit sum 87 in base 10.
4079899757679 is the difference of 2 nonnegative squares in 16 ways.
4079899757679 is the sum of 2 positive triangular numbers.
4079899757679 is the difference of 2 positive pentagonal numbers in 7 ways.
4079899757679 is not the sum of 3 positive squares.
40798997576792 = 28486882899962 + 29207117384552 = 19563708922652 + 35802506846042 = 18663856058042 + 36279728228252 = 27261976468712 + 30353629804202 = 21019149333002 + 34967893339292 = 17156472427292 + 37016397138602 = 25197795742952 + 32087837150042 = 23282662191962 + 33503370644252 = 14674321949852 + 38068654803962 = 27909345216962 + 29759480049752 = 20261210937452 + 35412448865042 = 8979558955352 + 39798564348962 = 27851275810712 + 29813833014002 = 17878212421292 + 36673256248802 = 6331516642712 + 40304715608402 = 25821458577752 + 31588138283042 = 15417148435052 + 37773929334962 = 3655827672152 + 40634875751042 = 20950939172252 + 35008803908042 = 9757361240552 + 39615048969962 = 2295055333352 + 40734394856042 = 18593092939292 + 36316044639002 = 7119740788712 + 40172969698202 = 4980287812712 + 40493887644602 = 16154059700252 + 37464710841962 = 4451031886952 + 40555474580042 = 7643773794152 + 40076563293962 = 24432447999962 + 32674358264552 = 13770572558042 + 38404811348252 = 1896617379962 + 40754889838952 = 22221175765802 + 34216626818792 = 11204118597002 + 39230420973212 = 799120159802 + 40791170738792 = 19912874450042 + 35609487982952 = 8588741691962 + 39884730404252 = 3491368329962 + 40649336408552 = 14520156635042 + 38127722913452 = 2694509766962 + 40709922873752 = 9368306664962 + 39708853339052 = 11970366037202 + 39003442671212 is the sum of 2 positive squares in 40 ways.
40798997576792 is the sum of 3 positive squares.
4079899757679 is a divisor of 1433466752 - 1.
4079899757679 = '407989' + '9757679' is the concatenation of 2 semiprime numbers.

Sunday, September 18, 2016

Number of the day: 659614

Adrien-Marie Legendre was born on this day 264 years ago.

Properties of the number 659614:

659614 = 2 × 271 × 1217 is a sphenic number and squarefree.
659614 has 3 distinct prime factors, 8 divisors, 29 antidivisors and 328320 totatives.
659614 has an emirp digit sum 31 in base 10.
659614 has an oblong digit product 6480 in base 10.
659614 is the sum of 2 positive triangular numbers.
659614 is the difference of 2 positive pentagonal numbers in 3 ways.
659614 = 182 + 1332 + 8012 is the sum of 3 positive squares.
6596142 = 3821102 + 5376642 is the sum of 2 positive squares in 1 way.
6596142 is the sum of 3 positive squares.
659614 is a divisor of 239216 - 1.

Saturday, September 17, 2016

Number of the day: 812676

Bernhard Riemann was born on this day 190 years ago.

Properties of the number 812676:

812676 = 22 × 3 × 67723 is the 747790th composite number and is not squarefree.
812676 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 270888 totatives.
812676 has a sphenic digit sum 30 in base 10.
812676 has an oblong digit sum 30 in base 10.
812676 has an oblong digit product 4032 in base 10.
812676 = 2031702 - 2031682 = 677262 - 677202 is the difference of 2 nonnegative squares in 2 ways.
812676 is the sum of 2 positive triangular numbers.
812676 is the difference of 2 positive pentagonal numbers in 1 way.
812676 = 762 + 1062 + 8922 is the sum of 3 positive squares.
8126762 is the sum of 3 positive squares.
812676 is a divisor of 24111287 - 1.

Friday, September 16, 2016

Number of the day: 8704198

Properties of the number 8704198:

8704198 = 2 × 97 × 44867 is a sphenic number and squarefree.
8704198 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 4307136 totatives.
8704198 has an emirp digit sum 37 in base 10.
8704198 is the difference of 2 positive pentagonal numbers in 4 ways.
8704198 = 732 + 2702 + 29372 is the sum of 3 positive squares.
87041982 = 58327102 + 64608482 is the sum of 2 positive squares in 1 way.
87041982 is the sum of 3 positive squares.
8704198 is a divisor of 97122433 - 1.

Thursday, September 15, 2016

Number of the day: 78859

Properties of the number 78859:

78859 = 11 × 67 × 107 is a sphenic number and squarefree.
78859 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 69960 totatives.
78859 has an emirp digit sum 37 in base 10.
Reversing the decimal digits of 78859 results in a sphenic number.
78859 = (11 × 12)/2 + … + (77 × 78)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
78859 = 394302 - 394292 = 35902 - 35792 = 6222 - 5552 = 4222 - 3152 is the difference of 2 nonnegative squares in 4 ways.
78859 is the sum of 2 positive triangular numbers.
78859 is the difference of 2 positive pentagonal numbers in 4 ways.
78859 = 172 + 272 + 2792 is the sum of 3 positive squares.
788592 is the sum of 3 positive squares.
78859 is a divisor of 85722 - 1.
78859 is palindromic in (at least) the following bases: -88, and -95.

The number 78859 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A058601: McKay-Thompson series of class 27b for the Monster group.

Wednesday, September 14, 2016

Number of the day: 64606

Properties of the number 64606:

64606 = 2 × 32303 is semiprime and squarefree.
64606 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 32302 totatives.
64606 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 64606 results in an emirpimes.
64606 is the sum of 2 positive triangular numbers.
64606 is the difference of 2 positive pentagonal numbers in 2 ways.
64606 = 92 + 742 + 2432 is the sum of 3 positive squares.
646062 is the sum of 3 positive squares.
64606 is a divisor of 229521 - 1.
64606 is an emirpimes in (at least) the following bases: 3, 8, 9, 10, 13, 14, 17, 25, 32, 41, 44, 52, 55, 58, 66, 68, 70, 73, 74, 84, 86, 89, 94, and 95.
64606 is palindromic in (at least) the following bases: 45, 54, 100, and -84.
64606 in base 45 = VeV and consists of only the digits 'V' and 'e'.
64606 in base 53 = Mqq and consists of only the digits 'M' and 'q'.
64606 in base 54 = M8M and consists of only the digits '8' and 'M'.

The number 64606 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A244985: Position of 2^n in A070003.

Tuesday, September 13, 2016

Number of the day: 667045920958924

Properties of the number 667045920958924:

667045920958924 = 22 × 13 × 649403 × 19753229 is composite and not squarefree.
667045920958924 has 4 distinct prime factors, 24 divisors, 107 antidivisors and 307866858471744 totatives.
667045920958924 = 1667614802397322 - 1667614802397302 = 128278061723002 - 128278061722742 = 2574413802 - 2561425742 = 281954682 - 113109902 is the difference of 2 nonnegative squares in 4 ways.
667045920958924 is the difference of 2 positive pentagonal numbers in 3 ways.
667045920958924 = 26582 + 1108822 + 258269942 is the sum of 3 positive squares.
6670459209589242 = 2565561234457402 + 6157346962697762 = 1354887196226242 + 6531409247038202 = 3683654043157762 + 5561089727483402 = 1261415375421242 + 6550103611199202 is the sum of 2 positive squares in 4 ways.
6670459209589242 is the sum of 3 positive squares.
667045920958924 is a divisor of 122312675677638 - 1.

Monday, September 12, 2016

Number of the day: 318

Properties of the number 318:

318 = 2 × 3 × 53 is a sphenic number and squarefree.
318 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 104 totatives.
318 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 318 results in a semiprime.
318 is the difference of 2 positive pentagonal numbers in 2 ways.
318 = 22 + 52 + 172 is the sum of 3 positive squares.
3182 = 1682 + 2702 is the sum of 2 positive squares in 1 way.
3182 is the sum of 3 positive squares.
318 is a divisor of 1072 - 1.
318 is palindromic in (at least) the following bases: 9, and 52.
318 in base 5 = 2233 and consists of only the digits '2' and '3'.
318 in base 7 = 633 and consists of only the digits '3' and '6'.
318 in base 9 = 383 and consists of only the digits '3' and '8'.
318 in base 12 = 226 and consists of only the digits '2' and '6'.
318 in base 17 = 11c and consists of only the digits '1' and 'c'.

The number 318 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000112: Number of partially ordered sets ("posets") with n unlabeled elements.
A005277: Nontotients: even n such that phi(m) = n has no solution.
A006313: Numbers n such that n^16 + 1 is prime.
A007304: Sphenic numbers: products of 3 distinct primes.
A008458: Coordination sequence for hexagonal lattice.
A008588: Nonnegative multiples of 6.
A034296: Number of flat partitions of n: partitions {a_i} with each |a_i-a_{i-1}| <= 1.
A119679: a(n) = least k such that the remainder when 5^k is divided by k is n.
A191426: Dispersion of (3+[nr]), where r=(golden ratio)=(1+sqrt(5))/2 and [ ]=floor, by antidiagonals.
A214899: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=2, a(1)=1, a(2)=2.

Sunday, September 11, 2016

Number of the day: 4454

Properties of the number 4454:

4454 = 2 × 17 × 131 is a sphenic number and squarefree.
4454 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 2080 totatives.
4454 has an emirp digit sum 17 in base 10.
4454 is the difference of 2 positive pentagonal numbers in 1 way.
4454 = 22 + 152 + 652 is the sum of 3 positive squares.
44542 = 20962 + 39302 is the sum of 2 positive squares in 1 way.
44542 is the sum of 3 positive squares.
4454 is a divisor of 5234 - 1.
4454 = '4' + '454' is the concatenation of 2 semiprime numbers.
4454 is palindromic in (at least) the following bases: 42, 61, -7, -22, -53, and -73.
4454 in base 3 = 20002222 and consists of only the digits '0' and '2'.
4454 consists of only the digits '4' and '5'.
4454 in base 16 = 1166 and consists of only the digits '1' and '6'.
4454 in base 18 = dd8 and consists of only the digits '8' and 'd'.
4454 in base 21 = a22 and consists of only the digits '2' and 'a'.
4454 in base 38 = 338 and consists of only the digits '3' and '8'.
4454 in base 41 = 2QQ and consists of only the digits '2' and 'Q'.
4454 in base 42 = 2M2 and consists of only the digits '2' and 'M'.
4454 in base 60 = 1EE and consists of only the digits '1' and 'E'.
4454 in base 61 = 1C1 and consists of only the digits '1' and 'C'.

The number 4454 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033014: Every run of digits of n in base 16 has length 2.
A033029: Every run of digits of n in base 16 has length >=2.
A058601: McKay-Thompson series of class 27b for the Monster group.
A069746: Four-digit numbers that do not resolve to 6174 under the Kaprekar map (see A151949).
A072522: Smallest number a(n)>a(n-1) such that T(a(n-1))+T(a(n))=T(m) for some m, a(1)=3; T(i) are the triangular numbers.
A077162: Sum of terms in n-th rows of triangle in A077159.
A118869: Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0101 (n,k>=0).
A118870: Number of binary sequences of length n with no subsequence 0101.
A252079: Fixed points of permutations A252022 and A252023.
A256290: Numbers which have only digits 4 and 5 in base 10.

Saturday, September 10, 2016

Number of the day: 37163

Properties of the number 37163:

37163 = 7 × 5309 is semiprime and squarefree.
37163 has 2 distinct prime factors, 4 divisors, 19 antidivisors and 31848 totatives.
37163 has an oblong digit sum 20 in base 10.
37163 has a triangular digit product 378 in base 10.
Reversing the decimal digits of 37163 results in an emirpimes.
37163 = 185822 - 185812 = 26582 - 26512 is the difference of 2 nonnegative squares in 2 ways.
37163 is the difference of 2 positive pentagonal numbers in 2 ways.
37163 = 132 + 452 + 1872 is the sum of 3 positive squares.
371632 = 21632 + 371002 is the sum of 2 positive squares in 1 way.
371632 is the sum of 3 positive squares.
37163 is a divisor of 2111327 - 1.
37163 = '37' + '163' is the concatenation of 2 prime numbers.
37163 is an emirpimes in (at least) the following bases: 3, 5, 7, 9, 10, 12, 15, 16, 21, 25, 31, 38, 40, 44, 46, 51, 52, 53, 57, 59, 66, 67, 69, 70, 72, 77, 79, 81, 89, 91, 93, 95, and 98.
37163 is palindromic in (at least) base 73.
37163 in base 51 = EEZ and consists of only the digits 'E' and 'Z'.

Friday, September 9, 2016

Number of the day: 83192211

Properties of the number 83192211:

83192211 = 33 × 1231 × 2503 is the 78347423th composite number and is not squarefree.
83192211 has 3 distinct prime factors, 16 divisors, 23 antidivisors and 55394280 totatives.
83192211 = 415961062 - 415961052 = 138653702 - 138653672 = 46217942 - 46217852 = 15406102 - 15405832 = 344062 - 331752 = 178702 - 153672 = 131102 - 94172 = 92942 - 17852 is the difference of 2 nonnegative squares in 8 ways.
83192211 is the sum of 2 positive triangular numbers.
83192211 is the difference of 2 positive pentagonal numbers in 1 way.
83192211 = 852 + 3192 + 91152 is the sum of 3 positive squares.
831922112 is the sum of 3 positive squares.
83192211 is a divisor of 571738 - 1.
83192211 = '8319' + '2211' is the concatenation of 2 sphenic numbers.

Thursday, September 8, 2016

Number of the day: 89125

Marin Mersenne was born on this day 428 years ago.

Properties of the number 89125:

89125 = 53 × 23 × 31 is the 80489th composite number and is not squarefree.
89125 has 3 distinct prime factors, 16 divisors, 17 antidivisors and 66000 totatives.
89125 has a semiprime digit sum 25 in base 10.
Reversing the decimal digits of 89125 results in a semiprime.
89125 = 445632 - 445622 = 89152 - 89102 = 19492 - 19262 = 17952 - 17702 = 14532 - 14222 = 4452 - 3302 = 4192 - 2942 = 3652 - 2102 is the difference of 2 nonnegative squares in 8 ways.
89125 is the sum of 2 positive triangular numbers.
89125 is the difference of 2 positive pentagonal numbers in 6 ways.
89125 = 332 + 402 + 2942 is the sum of 3 positive squares.
891252 = 534752 + 713002 = 249552 + 855602 = 313722 + 834212 is the sum of 2 positive squares in 3 ways.
891252 is the sum of 3 positive squares.
89125 is a divisor of 11515 - 1.
89125 is palindromic in (at least) the following bases: -53, -56, and -60.
89125 in base 22 = 8833 and consists of only the digits '3' and '8'.
89125 in base 52 = Wnn and consists of only the digits 'W' and 'n'.
89125 in base 54 = UUP and consists of only the digits 'P' and 'U'.
89125 in base 55 = TPP and consists of only the digits 'P' and 'T'.
89125 in base 59 = PZZ and consists of only the digits 'P' and 'Z'.

The number 89125 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A027447: Cube of the lower triangular mean matrix.
A027453: Third diagonal of A027447.
A125500: Expansion of -LambertW(-x^2*exp(x))/x^2.
A214092: Principal diagonal of the convolution array A213773.

Wednesday, September 7, 2016

Number of the day: 1532

Properties of the number 1532:

1532 = 22 × 383 is the 1289th composite number and is not squarefree.
1532 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 764 totatives.
1532 has a prime digit sum 11 in base 10.
1532 has a sphenic digit product 30 in base 10.
1532 has an oblong digit product 30 in base 10.
Reversing the decimal digits of 1532 results in a prime.
1532 = 3842 - 3822 is the difference of 2 nonnegative squares in 1 way.
1532 is the difference of 2 positive pentagonal numbers in 1 way.
1532 is not the sum of 3 positive squares.
15322 is the sum of 3 positive squares.
1532 is a divisor of 15312 - 1.
1532 = '1' + '532' is the concatenation of 2 pentagonal numbers.
1532 is palindromic in (at least) the following bases: -30, and -34.
1532 in base 3 = 2002202 and consists of only the digits '0' and '2'.
1532 in base 5 = 22112 and consists of only the digits '1' and '2'.
1532 in base 17 = 552 and consists of only the digits '2' and '5'.
1532 in base 19 = 44c and consists of only the digits '4' and 'c'.
1532 in base 22 = 33e and consists of only the digits '3' and 'e'.
1532 in base 27 = 22k and consists of only the digits '2' and 'k'.

The number 1532 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000084: Number of series-parallel networks with n unlabeled edges. Also called yoke-chains by Cayley and MacMahon.
A017817: a(0)=1, a(1)=a(2)=0, a(3)=1; a(n) = a(n-3) + a(n-4).
A058951: Coefficients of monic primitive irreducible polynomials over GF(7) listed in lexicographic order.
A097037: Initial values for iteration of A063919[x] function such that iteration ends in a 2-cycle i.e. "attracted" by unitary sociable numbers, A063991.
A161330: Snowflake (or E-toothpick) sequence (see Comments lines for definition).
A184943: Number of connected 4-regular simple graphs on n vertices with girth exactly 3.
A186733: Triangular array C(n,r) = number of connected r-regular graphs, having girth exactly 3, with n nodes, for 0 <= r < n.
A199847: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no element more than one greater than the previous
A217729: Trajectory of 40 under the map n-> A006369(n).
A262163: Number A(n,k) of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= k; square array A(n,k), n>=0, k>=0, read by antidiagonals.

Tuesday, September 6, 2016

Number of the day: 907362

Properties of the number 907362:

907362 = 2 × 35 × 1867 is the 835549th composite number and is not squarefree.
907362 has 3 distinct prime factors, 24 divisors, 23 antidivisors and 302292 totatives.
907362 = 192 + 802 + 9492 is the sum of 3 positive squares.
9073622 is the sum of 3 positive squares.
907362 is a divisor of 1033162 - 1.
907362 = '9073' + '62' is the concatenation of 2 semiprime numbers.

Monday, September 5, 2016

Number of the day: 516838

Properties of the number 516838:

516838 = 2 × 7 × 19 × 29 × 67 is the 474028th composite number and is squarefree.
516838 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 199584 totatives.
516838 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 516838 results in a sphenic number.
516838 is the sum of 2 positive triangular numbers.
516838 is the difference of 2 positive pentagonal numbers in 11 ways.
516838 = 302 + 432 + 7172 is the sum of 3 positive squares.
5168382 = 3564402 + 3742622 is the sum of 2 positive squares in 1 way.
5168382 is the sum of 3 positive squares.
516838 is a divisor of 17416 - 1.

Sunday, September 4, 2016

Number of the day: 2393783635

Properties of the number 2393783635:

2393783635 = 5 × 37 × 139 × 93089 is the 2277252976th composite number and is squarefree.
2393783635 has 4 distinct prime factors, 16 divisors, 25 antidivisors and 1849844736 totatives.
2393783635 has an emirpimes digit sum 49 in base 10.
2393783635 = 11968918182 - 11968918172 = 2393783662 - 2393783612 = 323484462 - 323484092 = 86108022 - 86106632 = 64697782 - 64695932 = 17224942 - 17217992 = 2352942 - 2301512 = 594022 - 336872 is the difference of 2 nonnegative squares in 8 ways.
2393783635 is the sum of 2 positive triangular numbers.
2393783635 is the difference of 2 positive pentagonal numbers in 7 ways.
2393783635 = 1052 + 7132 + 489212 is the sum of 3 positive squares.
23937836352 = 14476271762 + 19064563072 = 13339039092 + 19876872122 = 6171456832 + 23128621442 = 8940007402 + 22205771252 = 1254892002 + 23904921152 = 6565887402 + 23019755252 = 15346866292 + 18371001722 = 12400612562 + 20475468672 = 8559143232 + 22355336642 = 14362701812 + 19150269082 = 13456945842 + 19797237632 = 7375441472 + 22773292962 = 7763622602 + 22643899252 is the sum of 2 positive squares in 13 ways.
23937836352 is the sum of 3 positive squares.
2393783635 is a divisor of 18152362 - 1.
2393783635 = '239378' + '3635' is the concatenation of 2 semiprime numbers.
2393783635 = '23937' + '83635' is the concatenation of 2 sphenic numbers.
2393783635 is palindromic in (at least) base -25.

Friday, September 2, 2016

Number of the day: 700947726392172

Properties of the number 700947726392172:

700947726392172 = 22 × 3 × 7 × 19 × 569 × 15761 × 48973 is composite and not squarefree.
700947726392172 has 7 distinct prime factors, 192 divisors, 83 antidivisors and 189380882718720 totatives.
700947726392172 has a sphenic digit sum 66 in base 10.
700947726392172 has a triangular digit sum 66 in base 10.
700947726392172 is the difference of 2 nonnegative squares in 32 ways.
700947726392172 is the sum of 2 positive triangular numbers.
700947726392172 is the difference of 2 positive pentagonal numbers in 15 ways.
700947726392172 = 228982 + 490822 + 264753622 is the sum of 3 positive squares.
7009477263921722 = 4505543056650722 + 5369623197031802 = 1937608841729402 + 6736352387597282 = 3078073139490722 + 6297478643185802 = 1557963776321402 + 6834143719962722 = 1350696020429282 + 6878109607576202 = 4198292377853282 + 5613119687259002 = 2886331147749002 + 6387633679146722 = 44549766162722 + 7009335691188602 = 4665776833086602 + 5230993983677282 = 4233882593270402 + 5586323451057722 = 1601367717585722 + 6824103820027202 = 3386399500008002 + 6137187461678282 = 2845675303982282 + 6405849169137602 is the sum of 2 positive squares in 13 ways.
7009477263921722 is the sum of 3 positive squares.
700947726392172 is a divisor of 39710431036 - 1.

Thursday, September 1, 2016

Number of the day: 147006

Properties of the number 147006:

147006 = 2 × 32 × 8167 is the 133414th composite number and is not squarefree.
147006 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 48996 totatives.
147006 = 112 + 142 + 3832 is the sum of 3 positive squares.
1470062 is the sum of 3 positive squares.
147006 is a divisor of 371361 - 1.

The number 147006 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A207529: Number of n X n 0..3 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column
A207530: Number of nX3 0..3 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column
A207535: T(n,k)=Number of nXk 0..3 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column