Number of the day: 49583731785

Properties of the number 49583731785:

49583731785 = 3 × 5 × 7 × 17 × 421 × 65981 is composite and squarefree.
49583731785 has 6 distinct prime factors, 64 divisors, 107 antidivisors and 21282508800 totatives.
49583731785 is the difference of 2 nonnegative squares in 32 ways.
49583731785 is the difference of 2 positive pentagonal numbers in 14 ways.
49583731785 = 1805² + 5612² + 222596² is the sum of 3 positive squares.
49583731785² = 29750239071² + 39666985428² = 26947168248² + 41622068439² = 32411978592² + 37523460681² = 22180230072² + 44346181929² = 19072820319² + 45768700908² = 25182270561² + 42712992252² = 8876089929² + 48782799072² = 5494671252² + 49278342561² = 12215341908² + 48055508319² = 30788455383² + 38866662744² = 28038047604² + 40895162847² = 33392599716² + 36653522913² = 21000168756² + 44917027617² = 17856240087² + 46256903784² = 24044334153² + 43363768896² = 2119418847² + 49538414604² = 1298000256² + 49566739383² = 4709253087² + 49359592716² = 28691228727² + 40439582736² = 25837454076² + 42319882143² = 31408703004² + 38367171297² = 7583394273² + 49000393764² = 4190057424² + 49406374857² = 10940705496² + 48361631703² = 15124767273² + 47220629736² = 11836113996² + 48150315297² = 18341568924² + 46066618143² = 28701643425² + 40432191660² = 25848353160² + 42313226025² = 31418583840² + 38359080375² = 23333520840² + 43750351575² = 20264414625² + 45253728660² = 26291778975² + 42039134340² = 2106659625² + 49538958840² = 1310766660² + 49566403425² = 4721966025² + 49358378160² = 22168807500² + 44351893215² = 19061031465² + 45773611800² = 25171268535² + 42719476800² = 3415506465² + 49465955700² is the sum of 2 positive squares in 40 ways.
49583731785² is the sum of 3 positive squares.
49583731785 is a proper divisor of 13⁶⁵⁹⁸⁰ - 1.
49583731785 = '495837317' + '85' is the concatenation of 2 semiprime numbers.
49583731785 = '4958' + '3731785' is the concatenation of 2 sphenic numbers.

Number of the day: 507184197

Properties of the number 507184197:

507184197 = 3 × 13 × 37 × 351479 is the 480470281^th composite number and is squarefree.
507184197 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 303676992 totatives.
507184197 has a sphenic digit sum 42 in base 10.
507184197 has an oblong digit sum 42 in base 10.
507184197 = 253592099² - 253592098² = 84530701² - 84530698² = 19507091² - 19507078² = 6853859² - 6853822² = 6502381² - 6502342² = 2284669² - 2284558² = 527459² - 526978² = 176461² - 175018² is the difference of 2 nonnegative squares in 8 ways.
507184197 is the sum of 2 positive triangular numbers.
507184197 is the difference of 2 positive pentagonal numbers in 4 ways.
507184197 = 79² + 166² + 22520² is the sum of 3 positive squares.
507184197² = 336365403² + 379597320² = 195070845² + 468170028² = 32687547² + 506129760² = 164492172² + 479768835² is the sum of 2 positive squares in 4 ways.
507184197² is the sum of 3 positive squares.
507184197 is a proper divisor of 317¹¹¹⁶ - 1.
507184197 = '5071' + '84197' is the concatenation of 2 semiprime numbers.

Number of the day: 24323

Properties of the number 24323:

24323 is a cyclic number.
24323 = 13 × 1871 is semiprime and squarefree.
24323 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 22440 totatives.
24323 has a semiprime digit sum 14 in base 10.
24323 has a Fibonacci digit product 144 in base 10.
Reversing the decimal digits of 24323 results in a sphenic number.
24323 = 12162² - 12161² = 942² - 929² is the difference of 2 nonnegative squares in 2 ways.
24323 is the difference of 2 positive pentagonal numbers in 2 ways.
24323 = 3² + 17² + 155² is the sum of 3 positive squares.
24323² = 9355² + 22452² is the sum of 2 positive squares in 1 way.
24323² is the sum of 3 positive squares.
24323 is a proper divisor of 1483¹¹ - 1.
24323 is an emirpimes in (at least) the following bases: 2, 3, 4, 8, 16, 17, 18, 22, 23, 26, 31, 33, 35, 39, 41, 42, 43, 47, 48, 49, 50, 56, 57, 58, 59, 69, 73, 75, 79, 82, 84, 85, 86, 88, 91, 96, and 98.
24323 is palindromic in (at least) the following bases: 80, -83, and -95.

The number 24323 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A009939: Coordination sequence for MgZn2, Mg position.
A068055: Partial sums of A066425.
A075288: Interprimes (A024675) which are of the form s*prime, s=13.
A075461: Sorted list of solutions to the n-term Znam problem.
A156635: 144*n^2 - n.
A158550: a(n) = 169*n^2 - 13.
A217924: Row sums of triangle A217537.
A274075: Sum of n-th powers of the roots of x^3 + x^2 - 9*x - 1.
A292754: Numerators of coefficients in an asymptotic expansion of the Wallis sequence in inverse powers of n.

Number of the day: 29815

Properties of the number 29815:

29815 is a cyclic number.
29815 = 5 × 67 × 89 is a sphenic number and squarefree.
29815 has 3 distinct prime factors, 8 divisors, 21 antidivisors and 23232 totatives.
29815 has a semiprime digit sum 25 in base 10.
29815 = 14908² - 14907² = 2984² - 2979² = 256² - 189² = 212² - 123² is the difference of 2 nonnegative squares in 4 ways.
29815 is the difference of 2 positive pentagonal numbers in 3 ways.
29815 is not the sum of 3 positive squares.
29815² = 13065² + 26800² = 5628² + 29279² = 13601² + 26532² = 17889² + 23852² is the sum of 2 positive squares in 4 ways.
29815² is the sum of 3 positive squares.
29815 is a proper divisor of 461¹¹ - 1.
29815 = '298' + '15' is the concatenation of 2 semiprime numbers.
29815 is palindromic in (at least) the following bases: 39, 43, and -69.
29815 in base 16 = 7477 and consists of only the digits '4' and '7'.
29815 in base 39 = JNJ and consists of only the digits 'J' and 'N'.
29815 in base 42 = Gbb and consists of only the digits 'G' and 'b'.
29815 in base 43 = G5G and consists of only the digits '5' and 'G'.

The number 29815 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A034858: a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15.
A034859: a(n) = C(n+3,4) + 3*C(n+1,3) + 5*C(n-1,2) + 7*n - 15 for n >= 3; a(1)=1, a(2)=10.
A184261: Number of strings of numbers x(i=1..6) in 0..n with sum i^3*x(i) equal to 216*n
A269874: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 41", based on the 5-celled von Neumann neighborhood.

Number of the day: 9757

Shiing-Shen Chern was born on this day 107 years ago.

Properties of the number 9757:

9757 is a cyclic number.
9757 = 11 × 887 is semiprime and squarefree.
9757 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 8860 totatives.
9757 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 9757 results in a sphenic number.
9757 = 12³ + 13³ + 18³ is the sum of 3 positive cubes in 1 way.
9757 = 4879² - 4878² = 449² - 438² is the difference of 2 nonnegative squares in 2 ways.
9757 is the difference of 2 positive pentagonal numbers in 2 ways.
9757 = 10² + 21² + 96² is the sum of 3 positive squares.
9757² is the sum of 3 positive squares.
9757 is a proper divisor of 353⁴⁴³ - 1.
9757 is an emirpimes in (at least) the following bases: 5, 12, 13, 14, 16, 18, 20, 21, 23, 25, 31, 37, 40, 41, 42, 43, 44, 45, 47, 51, 57, 63, 64, 67, 71, 73, 75, 77, 79, 80, 83, 84, 89, 90, 96, 98, and 99.
9757 is palindromic in (at least) the following bases: 9, -28, -39, and -46.
9757 in base 3 = 111101101 and consists of only the digits '0' and '1'.
9757 in base 25 = ff7 and consists of only the digits '7' and 'f'.
9757 in base 27 = daa and consists of only the digits 'a' and 'd'.
9757 in base 28 = ccd and consists of only the digits 'c' and 'd'.

The number 9757 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A050069: a(n) = a(n-1)+a(m), where m=2^(p+1)+2-n and 2^p<n-1<=2^(p+1), for n >= 4.
A056434: Number of step cyclic shifted sequence structures using exactly two different symbols.
A084476: Least k such that 10^(2n-1)+k is a brilliant number.
A136780: Number of primitive multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2.
A192160: Monotonic ordering of nonnegative differences 10^i-3^j, for i>=0, j>=0.
A228930: Optimal ascending continued fraction expansion of e - 2.
A258167: Indices of the start of 9 successive distinct digits in the decimal expansion of e (2.718281828...).
A268306: The number of even permutations p of 1,2,...,n such that -1<=p(i)-i<=2 for i=1,2,...,n
A290100: Start from the singleton set S = {n}, and unless 1 is already a member of S, generate on each iteration a new set where each odd number k is replaced by 3k+1, and each even number k is replaced by 3k+1 and k/2. a(n) is the size of the set after the first iteration which has produced 1 as a member.
A316719: Expansion of Product_{k=1..7} (1+x^(2*k-1))/(1-x^(2*k)).

Number of the day: 10232018

Happy Mole Day!

Properties of the number 10232018:

10232018 = 2 × 61 × 83869 is a sphenic number and squarefree.
10232018 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 5032080 totatives.
10232018 has an emirp digit sum 17 in base 10.
10232018 = 2053² + 2453² = 1577² + 2783² is the sum of 2 positive squares in 2 ways.
10232018 = 107² + 112² + 3195² is the sum of 3 positive squares.
10232018² = 1845118² + 10064280² = 1802400² + 10072018² = 5258160² + 8777582² = 3589118² + 9581880² is the sum of 2 positive squares in 4 ways.
10232018² is the sum of 3 positive squares.
10232018 is a proper divisor of 197¹⁴⁴⁶ - 1.
10232018 = '10' + '232018' is the concatenation of 2 semiprime numbers.
10232018 = '102' + '32018' is the concatenation of 2 sphenic numbers.

Number of the day: 344049

Properties of the number 344049:

344049 = 3 × 73 × 1571 is a sphenic number and squarefree.
344049 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 226080 totatives.
344049 = 172025² - 172024² = 57343² - 57340² = 2393² - 2320² = 895² - 676² is the difference of 2 nonnegative squares in 4 ways.
344049 is the sum of 2 positive triangular numbers.
344049 is the difference of 2 positive pentagonal numbers in 2 ways.
344049 = 13² + 22² + 586² is the sum of 3 positive squares.
344049² = 226224² + 259215² is the sum of 2 positive squares in 1 way.
344049² is the sum of 3 positive squares.
344049 is a proper divisor of 1607³¹⁴ - 1.

The number 344049 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A305158: a(n) = 21*2^n - 15.

Number of the day: 7768494

Martin Gardner was born on this day 104 years ago.

Properties of the number 7768494:

7768494 = 2 × 3³ × 263 × 547 is the 7243308^th composite number and is not squarefree.
7768494 has 4 distinct prime factors, 32 divisors, 17 antidivisors and 2574936 totatives.
7768494 has a triangular digit sum 45 in base 10.
7768494 is the difference of 2 positive pentagonal numbers in 2 ways.
7768494 = 13² + 110² + 2785² is the sum of 3 positive squares.
7768494² is the sum of 3 positive squares.
7768494 is a proper divisor of 1601⁷⁸⁶ - 1.
7768494 = '776849' + '4' is the concatenation of 2 semiprime numbers.

Number of the day: 1925

Properties of the number 1925:

1925 = 5² × 7 × 11 is the 1631^th composite number and is not squarefree.
1925 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 1200 totatives.
1925 has an emirp digit sum 17 in base 10.
1925 has an oblong digit product 90 in base 10.
Reversing the decimal digits of 1925 results in a sphenic number.
1925 = 5³ + … + 9³ is the sum of at least 2 consecutive cubes.
1925 = 963² - 962² = 195² - 190² = 141² - 134² = 93² - 82² = 51² - 26² = 45² - 10² is the difference of 2 nonnegative squares in 6 ways.
1925 is the difference of 2 positive pentagonal numbers in 5 ways.
1925 = 12² + 25² + 34² is the sum of 3 positive squares.
1925² = 1155² + 1540² = 539² + 1848² is the sum of 2 positive squares in 2 ways.
1925² is the sum of 3 positive squares.
1925 is a proper divisor of 43⁴ - 1.
1925 = '1' + '925' is the concatenation of 2 pentagonal numbers.
1925 is palindromic in (at least) the following bases: 37, 54, 76, -19, -20, -52, and -74.
1925 in base 15 = 885 and consists of only the digits '5' and '8'.
1925 in base 19 = 566 and consists of only the digits '5' and '6'.
1925 in base 36 = 1hh and consists of only the digits '1' and 'h'.
1925 in base 37 = 1F1 and consists of only the digits '1' and 'F'.
1925 in base 43 = 11X and consists of only the digits '1' and 'X'.

The number 1925 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000914: Stirling numbers of the first kind: s(n+2, n).
A001082: Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, ...
A002412: Hexagonal pyramidal numbers, or greengrocer's numbers.
A002623: G.f.: 1/((1-x)^4*(1+x)).
A029470: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 25 (most significant digit on left).
A033282: Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
A045944: Rhombic matchstick numbers: a(n) = n*(3*n+2).
A086810: Triangle obtained by adding a leading diagonal 1,0,0,0,... to A033282.
A115067: a(n) = (3*n^2 - n - 2)/2.
A303303: Generalized 23-gonal (or icositrigonal) numbers: m*(21*m - 19)/2 with m = 0, +1, -1, +2, -2, +3, -3, ...

Number of the day: 670097

Properties of the number 670097:

670097 is a cyclic number.
670097 and 670099 form a twin prime pair.
670097 has 9 antidivisors and 670096 totatives.
670097 has a prime digit sum 29 in base 10.
670097 = 335049² - 335048² is the difference of 2 nonnegative squares in 1 way.
670097 is the difference of 2 positive pentagonal numbers in 1 way.
670097 = 191² + 796² is the sum of 2 positive squares in 1 way.
670097 = 4² + 65² + 816² is the sum of 3 positive squares.
670097² = 304072² + 597135² is the sum of 2 positive squares in 1 way.
670097² is the sum of 3 positive squares.
670097 is a proper divisor of 911¹²⁴ - 1.
670097 = '6' + '70097' is the concatenation of 2 semiprime numbers.
670097 is an emirp in (at least) the following bases: 7, 15, 19, 45, 58, 79, 84, 86, 95, and 97.

The number 670097 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequence (among others):

Sequence number and description below are taken from OEIS.
A104962: Primes from merging of 6 successive digits in decimal expansion of cos(1).

Number of the day: 8277

Properties of the number 8277:

8277 = 3 × 31 × 89 is a sphenic number and squarefree.
8277 has 3 distinct prime factors, 8 divisors, 21 antidivisors and 5280 totatives.
8277 = 4139² - 4138² = 1381² - 1378² = 149² - 118² = 91² - 2² is the difference of 2 nonnegative squares in 4 ways.
8277 is the sum of 2 positive triangular numbers.
8277 is the difference of 2 positive pentagonal numbers in 1 way.
8277 = 16² + 25² + 86² is the sum of 3 positive squares.
8277² = 3627² + 7440² is the sum of 2 positive squares in 1 way.
8277² is the sum of 3 positive squares.
8277 is a proper divisor of 1301⁴ - 1.
8277 = '827' + '7' is the concatenation of 2 prime numbers.
8277 = '82' + '77' is the concatenation of 2 semiprime numbers.
8277 is palindromic in (at least) the following bases: 92, and -44.
8277 in base 14 = 3033 and consists of only the digits '0' and '3'.
8277 in base 52 = 339 and consists of only the digits '3' and '9'.

The number 8277 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003185: a(n) = (4*n+1)(4*n+5).
A067598: Decimal encoding of the prime factorization of n is a multiple of n.
A078371: a(n) = (2*n+5)*(2*n+1).
A101049: Number of partitions of n into parts having at most two prime-factors.
A111473: a(1) = 3, a(n) = least k such that concatenation of n copies of k with all previous concatenation gives a prime.
A142600: Third trisection of A061037.
A209774: Triangle of coefficients of polynomials v(n,x) jointly generated with A209773; see the Formula section.
A251268: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having x11-x00 less than x10-x01
A269910: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 3", based on the 5-celled von Neumann neighborhood.
A273831: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 961", based on the 5-celled von Neumann neighborhood.

Number of the day: 701

Properties of the number 701:

701 is a cyclic number.
701 is the 126^th prime.
701 has 5 antidivisors and 700 totatives.
701 has a Fibonacci digit sum 8 in base 10.
701 has sum of divisors equal to 702 which is an oblong number.
Reversing the decimal digits of 701 results in an emirp.
701 = 4³ + 5³ + 8³ is the sum of 3 positive cubes in 1 way.
701 = 351² - 350² is the difference of 2 nonnegative squares in 1 way.
701 is the difference of 2 positive pentagonal numbers in 1 way.
701 = 5² + 26² is the sum of 2 positive squares in 1 way.
701 = 12² + 14² + 19² is the sum of 3 positive squares.
701² = 260² + 651² is the sum of 2 positive squares in 1 way.
701² is the sum of 3 positive squares.
701 is a proper divisor of 89⁵ - 1.
701 = '70' + '1' is the concatenation of 2 pentagonal numbers.
701 is an emirp in (at least) the following bases: 2, 3, 7, 10, 11, 14, 17, 23, 24, 26, 27, 28, 30, 36, 39, 40, 41, 46, 51, 55, 59, 67, 69, 73, 76, 83, 87, 88, 89, 90, 93, 94, 96, 97, and 100.
701 is palindromic in (at least) the following bases: 5, 9, 20, 25, -5, -7, -12, -28, -35, -50, -70, and -100.
701 in base 3 = 221222 and consists of only the digits '1' and '2'.
701 in base 9 = 858 and consists of only the digits '5' and '8'.
701 in base 11 = 588 and consists of only the digits '5' and '8'.
701 in base 18 = 22h and consists of only the digits '2' and 'h'.
701 in base 19 = 1hh and consists of only the digits '1' and 'h'.
701 in base 20 = 1f1 and consists of only the digits '1' and 'f'.
701 in base 24 = 155 and consists of only the digits '1' and '5'.
701 in base 25 = 131 and consists of only the digits '1' and '3'.

The number 701 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000978: Wagstaff numbers: numbers n such that (2^n + 1)/3 is prime.
A001122: Primes with primitive root 2.
A006567: Emirps (primes whose reversal is a different prime).
A007500: Primes whose reversal in base 10 is also prime (called "palindromic primes" by D. Wells, although that name usually refers to A002385). Also called reversible primes.
A028387: a(n) = n + (n+1)^2.
A030430: Primes of the form 10*n+1.
A034856: a(n) = binomial(n+1, 2) + n - 1 = n(n + 3)/2 - 1.
A139827: Primes of the form 2x^2+2xy+17y^2.
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.
A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.

Number of the day: 948439501360

Properties of the number 948439501360:

948439501360 = 2⁴ × 5 × 13 × 16901 × 53959 is composite and not squarefree.
948439501360 has 5 distinct prime factors, 80 divisors, 27 antidivisors and 350165836800 totatives.
948439501360 is the difference of 2 nonnegative squares in 24 ways.
948439501360 is the sum of 2 positive triangular numbers.
948439501360 is the difference of 2 positive pentagonal numbers in 8 ways.
948439501360 = 7204² + 8820² + 973812² is the sum of 3 positive squares.
948439501360² = 557323949104² + 767416121472² = 219292829376² + 922739477168² = 494028747088² + 809612922816² = 351273090000² + 880990751360² = 14590513600² + 948327266640² = 378209422800² + 869767279360² = 580668770864² + 749907505152² = 247575978816² + 915556455088² = 468888169808² + 824427905856² = 569063700816² + 758751601088² = 233462031104² + 919256747472² = 481515439152² + 817117108864² = 364784423600² + 875482616640² is the sum of 2 positive squares in 13 ways.
948439501360² is the sum of 3 positive squares.
948439501360 is a proper divisor of 1697⁴¹²⁶²⁰ - 1.

Number of the day: 6065

Properties of the number 6065:

6065 is a cyclic number.
6065 = 5 × 1213 is semiprime and squarefree.
6065 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 4848 totatives.
6065 has an emirp digit sum 17 in base 10.
Reversing the decimal digits of 6065 results in an emirpimes.
6065 = 3033² - 3032² = 609² - 604² is the difference of 2 nonnegative squares in 2 ways.
6065 is the difference of 2 positive pentagonal numbers in 2 ways.
6065 = 32² + 71² = 17² + 76² is the sum of 2 positive squares in 2 ways.
6065 = 16² + 25² + 72² is the sum of 3 positive squares.
6065² = 3639² + 4852² = 2584² + 5487² = 4017² + 4544² = 1225² + 5940² is the sum of 2 positive squares in 4 ways.
6065² is the sum of 3 positive squares.
6065 is a proper divisor of 1931⁴ - 1.
6065 is an emirpimes in (at least) the following bases: 2, 4, 10, 11, 12, 13, 15, 17, 19, 23, 25, 29, 33, 34, 37, 38, 41, 45, 49, 58, 61, 63, 65, 74, 77, 91, 95, and 98.
6065 is palindromic in (at least) base 47.
6065 in base 27 = 88h and consists of only the digits '8' and 'h'.
6065 in base 46 = 2dd and consists of only the digits '2' and 'd'.
6065 in base 47 = 2Z2 and consists of only the digits '2' and 'Z'.

The number 6065 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A031127: Number of proper factorizations of p1^n*p2^4, where p1 and p2 are distinct primes.
A046874: Row/column pre-periods of Sprague-Grundy values of Wythoff's Game.
A061294: a(n) = floor( n^Pi ).
A080298: Positions of A080299 in A014486.
A095383: Number of different initial values for 3x+1 trajectories started with initial values not exceeding 2^n and in which the peak values are larger than 2^n.
A116702: Number of permutations of length n which avoid the patterns 123, 3241.
A192706: Number of 6X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 6 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations)
A248987: T(n,k)=Number of length n+4 0..k arrays with every five consecutive terms having two times the sum of some three elements equal to three times the sum of the remaining two
A294548: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
A296275: Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1)*b(n), where a(0) = 2, a(1) = 3, b(0) = 1, b(1) = 4, b(2) = 5, and (a(n)) and (b(n)) are increasing complementary sequences.

Number of the day: 3201726671

Properties of the number 3201726671:

3201726671 = 11² × 13 × 17² × 7043 is the 3048046956^th composite number and is not squarefree.
3201726671 has 4 distinct prime factors, 36 divisors, 51 antidivisors and 2528359680 totatives.
3201726671 has a semiprime digit sum 35 in base 10.
3201726671 is the difference of 2 nonnegative squares in 18 ways.
3201726671 is the difference of 2 positive pentagonal numbers in 17 ways.
3201726671 is not the sum of 3 positive squares.
3201726671² = 1783660879² + 2658873360² = 623812596² + 3140368055² = 1768321225² + 2669099796² = 1506694904² + 2825052945² = 304236471² + 3187239220² = 2028243140² + 2477354121² = 1231433335² + 2955440004² is the sum of 2 positive squares in 7 ways.
3201726671² is the sum of 3 positive squares.
3201726671 is a proper divisor of 1429¹⁸⁸¹²² - 1.
3201726671 = '32017' + '26671' is the concatenation of 2 semiprime numbers.
3201726671 = '3201' + '726671' is the concatenation of 2 sphenic numbers.

Number of the day: 177372

Properties of the number 177372:

177372 = 2² × 3² × 13 × 379 is the 161259^th composite number and is not squarefree.
177372 has 4 distinct prime factors, 36 divisors, 13 antidivisors and 54432 totatives.
177372 = 44344² - 44342² = 14784² - 14778² = 4936² - 4918² = 3424² - 3398² = 1176² - 1098² = 496² - 262² is the difference of 2 nonnegative squares in 6 ways.
177372 is the difference of 2 positive pentagonal numbers in 2 ways.
177372 is not the sum of 3 positive squares.
177372² = 68220² + 163728² is the sum of 2 positive squares in 1 way.
177372² is the sum of 3 positive squares.
177372 is a proper divisor of 757⁶ - 1.
177372 = '17737' + '2' is the concatenation of 2 prime numbers.
177372 is palindromic in (at least) base -93.
177372 in base 35 = 44rr and consists of only the digits '4' and 'r'.

Number of the day: 777907067

Properties of the number 777907067:

777907067 is a cyclic number.
777907067 = 7 × 111129581 is semiprime and squarefree.
777907067 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 666777480 totatives.
Reversing the decimal digits of 777907067 results in an emirpimes.
777907067 = 388953534² - 388953533² = 55564794² - 55564787² is the difference of 2 nonnegative squares in 2 ways.
777907067 is the difference of 2 positive pentagonal numbers in 2 ways.
777907067 = 165² + 289² + 27889² is the sum of 3 positive squares.
777907067² = 19184620² + 777670467² is the sum of 2 positive squares in 1 way.
777907067² is the sum of 3 positive squares.
777907067 is a proper divisor of 1289^5556479 - 1.
777907067 is an emirpimes in (at least) the following bases: 9, 10, 11, 12, 19, 25, 33, 42, 43, 46, 47, 49, 54, 56, 59, 60, 65, 69, 74, 77, 79, 80, and 100.

Number of the day: 857236

Properties of the number 857236:

857236 = 2² × 214309 is the 789091^th composite number and is not squarefree.
857236 has 2 distinct prime factors, 6 divisors, 9 antidivisors and 428616 totatives.
857236 has an emirp digit sum 31 in base 10.
Reversing the decimal digits of 857236 results in a sphenic number.
857236 = 214310² - 214308² is the difference of 2 nonnegative squares in 1 way.
857236 is the difference of 2 positive pentagonal numbers in 1 way.
857236 = 606² + 700² is the sum of 2 positive squares in 1 way.
857236 = 34² + 156² + 912² is the sum of 3 positive squares.
857236² = 122764² + 848400² is the sum of 2 positive squares in 1 way.
857236² is the sum of 3 positive squares.
857236 is a proper divisor of 29⁵⁹⁵³ - 1.
857236 = '85723' + '6' is the concatenation of 2 semiprime numbers.

Number of the day: 5197932510

Properties of the number 5197932510:

5197932510 = 2 × 3 × 5 × 173264417 is the 4954122512^th composite number and is squarefree.
5197932510 has 4 distinct prime factors, 16 divisors, 15 antidivisors and 1386115328 totatives.
5197932510 has a sphenic digit sum 42 in base 10.
5197932510 has an oblong digit sum 42 in base 10.
5197932510 is the difference of 2 positive pentagonal numbers in 2 ways.
5197932510 = 1010² + 1237² + 72079² is the sum of 3 positive squares.
5197932510² = 3072552264² + 4192603602² = 57520350² + 5197614240² = 3164584824² + 4123579182² = 3118759506² + 4158346008² is the sum of 2 positive squares in 4 ways.
5197932510² is the sum of 3 positive squares.
5197932510 is a proper divisor of 263^1666004 - 1.

Number of the day: 3470

Properties of the number 3470:

3470 = 2 × 5 × 347 is a sphenic number and squarefree.
3470 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 1384 totatives.
3470 has a semiprime digit sum 14 in base 10.
3470 = 33² + … + 35² is the sum of at least 2 consecutive positive squares in 1 way.
3470 is the difference of 2 positive pentagonal numbers in 2 ways.
3470 = 6² + 25² + 53² is the sum of 3 positive squares.
3470² = 2082² + 2776² is the sum of 2 positive squares in 1 way.
3470² is the sum of 3 positive squares.
3470 is a proper divisor of 11¹⁷³ - 1.
3470 is palindromic in (at least) the following bases: -16, and -51.
3470 in base 8 = 6616 and consists of only the digits '1' and '6'.
3470 in base 41 = 22Q and consists of only the digits '2' and 'Q'.
3470 in base 58 = 11m and consists of only the digits '1' and 'm'.

The number 3470 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005914: Number of points on surface of hexagonal prism: 12n^2 + 2 for n>0 (coordination sequence for W(2)).
A005918: Number of points on surface of square pyramid: 3*n^2 + 2 (n>0).
A051230: Bernoulli number B_{n} has denominator 66.
A061658: In base 4 n and n^2 contain the same digits in the same proportion.
A116636: Positive integers k such that 13^k == 9 (mod k).
A120328: Sum of three consecutive squares: n^2 + (n + 1)^2 + (n + 2)^2.
A129221: Residues of the Lucas - Lehmer primality test for M(13) = 8191.
A135885: Triangle Q, read by rows, where column k of Q equals column 0 of Q^(k+1) and Q is equal to the matrix square of integer triangle P = A135880 such that column 0 of Q equals column 0 of P shift left.
A164770: Numbers n with property that average digit of n^2 is 2.
A260841: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 00000011 or 00010101