Number of the day: 6502

Properties of the number 6502:

6502 = 2 × 3251 is semiprime and squarefree.
6502 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 3250 totatives.
6502 has an emirp digit sum 13 in base 10.
6502 has a Fibonacci digit sum 13 in base 10.
6502 is the difference of 2 positive pentagonal numbers in 2 ways.
6502 = 6² + 29² + 75² is the sum of 3 positive squares.
6502² is the sum of 3 positive squares.
6502 is a proper divisor of 1237¹⁰ - 1.
6502 = '6' + '502' is the concatenation of 2 semiprime numbers.
6502 = '650' + '2' is the concatenation of 2 oblong numbers.
6502 is an emirpimes in (at least) the following bases: 3, 6, 8, 9, 11, 22, 24, 31, 39, 44, 49, 51, 54, 55, 56, 58, 59, 60, 61, 62, 63, 68, 70, 73, 76, 77, 78, 79, 80, 82, 83, 84, 85, 88, 91, 92, 95, 96, 97, 98, and 100.
6502 is palindromic in (at least) the following bases: 32, 38, 50, 52, and -65.
6502 in base 4 = 1211212 and consists of only the digits '1' and '2'.
6502 in base 5 = 202002 and consists of only the digits '0' and '2'.
6502 in base 25 = aa2 and consists of only the digits '2' and 'a'.
6502 in base 28 = 886 and consists of only the digits '6' and '8'.
6502 in base 31 = 6nn and consists of only the digits '6' and 'n'.
6502 in base 32 = 6b6 and consists of only the digits '6' and 'b'.
6502 in base 37 = 4RR and consists of only the digits '4' and 'R'.
6502 in base 38 = 4J4 and consists of only the digits '4' and 'J'.
6502 in base 46 = 33G and consists of only the digits '3' and 'G'.
6502 in base 49 = 2YY and consists of only the digits '2' and 'Y'.

The number 6502 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006477: Number of partitions of n with at least 1 odd and 1 even part.
A017980: Powers of cube root of 2 rounded to nearest integer.
A017981: Powers of cube root of 2 rounded up.
A017986: Powers of cube root of 4 rounded to nearest integer.
A017987: Powers of cube root of 4 rounded up.
A047967: Number of partitions of n with some part repeated.
A101200: Number of partitions of n with rank 3 (the rank of a partition is the largest part minus the number of parts).
A186236: G.f.: exp( Sum_{n>=0} [ Sum_{k=0..2*n} A027907(n,k)^2 * x^k ]* x^n/n ), where A027907 is the triangle of trinomial coefficients.
A273366: a(n) = 10*n^2 + 10*n + 2.
A299281: Coordination sequence for "reo-e" 3D uniform tiling.

Number of the day: 81081

Properties of the number 81081:

81081 = 3⁴ × 7 × 11 × 13 is the 73143^th composite number and is not squarefree.
81081 has 4 distinct prime factors, 40 divisors, 43 antidivisors and 38880 totatives.
81081 is the difference of 2 nonnegative squares in 20 ways.
81081 is the sum of 2 positive triangular numbers.
81081 is the difference of 2 positive pentagonal numbers in 1 way.
81081 = 41² + 46² + 278² is the sum of 3 positive squares.
81081² = 31185² + 74844² is the sum of 2 positive squares in 1 way.
81081² is the sum of 3 positive squares.
81081 is a proper divisor of 1187⁶ - 1.
81081 is palindromic in (at least) base 54.
81081 in base 23 = 6f66 and consists of only the digits '6' and 'f'.
81081 in base 48 = Z99 and consists of only the digits '9' and 'Z'.
81081 in base 54 = RhR and consists of only the digits 'R' and 'h'.

The number 81081 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003913: Degrees of irreducible representations of Fischer group Fi22.
A064001: Odd abundant numbers not divisible by 5.
A104676: a(n) = binomial(n+2,2) * binomial(n+7,2).
A121738: Dimensions of the irreducible representations of the simple Lie algebra of type F4 over the complex numbers, listed in increasing order.
A144280: Lower triangular array called S2hat(-3) related to partition number array A144279.
A144282: Second column (m=2) of triangle S2hat(-3) = A144280.
A151338: Triangle read by rows: T(n,k) = number of partitions of [1..k] into n nonempty clumps of sizes 1, 2, 3, 4 or 5 (n >= 0, 0 <= k <= 5n).
A160654: Denominator of Laguerre(n, 10).
A239568: Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.
A275449: Least odd primitive abundant number with n prime factors, counted with multiplicity.

Number of the day: 1153

Properties of the number 1153:

1153 is a cyclic number.
1151 and 1153 form a twin prime pair.
1153 has 5 antidivisors and 1152 totatives.
1153 has a semiprime digit sum 10 in base 10.
1153 has a triangular digit sum 10 in base 10.
1153 has an emirpimes digit product 15 in base 10.
1153 has a triangular digit product 15 in base 10.
1153 has sum of divisors equal to 1154 which is an emirpimes.
Reversing the decimal digits of 1153 results in an emirp.
1153 = 577² - 576² is the difference of 2 nonnegative squares in 1 way.
1153 is the difference of 2 positive pentagonal numbers in 1 way.
1153 = 8² + 33² is the sum of 2 positive squares in 1 way.
1153 = 1² + 24² + 24² is the sum of 3 positive squares.
1153² = 528² + 1025² is the sum of 2 positive squares in 1 way.
1153² is the sum of 3 positive squares.
1153 is a proper divisor of 1013⁴ - 1.
1153 = '11' + '53' is the concatenation of 2 prime numbers.
1153 = '1' + '153' is the concatenation of 2 triangular numbers.
1153 is an emirp in (at least) the following bases: 2, 6, 7, 9, 10, 13, 26, 29, 30, 31, 34, 35, 39, 41, 43, 46, 49, 50, 53, 57, 59, 61, 65, 66, 71, 79, 81, 85, 86, 89, 91, and 97.
1153 is palindromic in (at least) the following bases: 11, 14, 32, -23, -36, -48, -64, -72, and -96.
1153 in base 11 = 959 and consists of only the digits '5' and '9'.
1153 in base 14 = 5c5 and consists of only the digits '5' and 'c'.
1153 in base 19 = 33d and consists of only the digits '3' and 'd'.
1153 in base 31 = 166 and consists of only the digits '1' and '6'.
1153 in base 32 = 141 and consists of only the digits '1' and '4'.
1153 in base 33 = 11v and consists of only the digits '1' and 'v'.

The number 1153 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005109: Class 1- (or Pierpont) primes: primes of the form 2^t*3^u + 1.
A005383: Numbers n such that both n and (n+1)/2 are primes.
A006450: Prime-indexed primes: primes with prime subscripts.
A006512: Greater of twin primes.
A006567: Emirps (primes whose reversal is a different prime).
A007519: Primes of form 8n+1, that is, primes congruent to 1 mod 8.
A058331: a(n) = 2*n^2 + 1.
A068228: Primes congruent to 1 (mod 12).
A160120: Y-toothpick sequence (see Comments lines for definition).
A235394: Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.

Number of the day: 2752347

Properties of the number 2752347:

2752347 = 3 × 13 × 70573 is a sphenic number and squarefree.
2752347 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 1693728 totatives.
2752347 has a sphenic digit sum 30 in base 10.
2752347 has an oblong digit sum 30 in base 10.
2752347 = 1376174² - 1376173² = 458726² - 458723² = 105866² - 105853² = 35306² - 35267² is the difference of 2 nonnegative squares in 4 ways.
2752347 is the sum of 2 positive triangular numbers.
2752347 is the difference of 2 positive pentagonal numbers in 2 ways.
2752347 = 71² + 91² + 1655² is the sum of 3 positive squares.
2752347² = 1058595² + 2540628² = 229680² + 2742747² = 1768197² + 2109240² = 1266915² + 2443428² is the sum of 2 positive squares in 4 ways.
2752347² is the sum of 3 positive squares.
2752347 is a proper divisor of 103¹¹⁷⁶² - 1.

Number of the day: 630192

Properties of the number 630192:

630192 = 2⁴ × 3 × 19 × 691 is the 578837^th composite number and is not squarefree.
630192 has 4 distinct prime factors, 40 divisors, 13 antidivisors and 198720 totatives.
630192 has a semiprime digit sum 21 in base 10.
630192 has a Fibonacci digit sum 21 in base 10.
630192 has a triangular digit sum 21 in base 10.
630192 = (248 × 249)/2 + … + (266 × 267)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
630192 is the difference of 2 nonnegative squares in 12 ways.
630192 is the sum of 2 positive triangular numbers.
630192 is the difference of 2 positive pentagonal numbers in 2 ways.
630192 = 68² + 172² + 772² is the sum of 3 positive squares.
630192² is the sum of 3 positive squares.
630192 is a proper divisor of 1129⁶ - 1.

Number of the day: 74698622

Properties of the number 74698622:

74698622 = 2 × 37349311 is semiprime and squarefree.
74698622 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 37349310 totatives.
Reversing the decimal digits of 74698622 results in an emirpimes.
74698622 = 50² + 171² + 8641² is the sum of 3 positive squares.
74698622² is the sum of 3 positive squares.
74698622 is a proper divisor of 439²⁰²⁶ - 1.
74698622 is an emirpimes in (at least) the following bases: 4, 6, 7, 10, 12, 13, 19, 29, 34, 40, 48, 50, 56, 58, 59, 60, 62, 67, 68, 70, 79, 80, 82, 84, 91, 93, 94, and 97.

Number of the day: 43661

Properties of the number 43661:

43661 is a cyclic number.
43661 is the 4550^th prime.
43661 has 7 antidivisors and 43660 totatives.
43661 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 43661 results in a semiprime.
43661 = 21831² - 21830² is the difference of 2 nonnegative squares in 1 way.
43661 is the sum of 2 positive triangular numbers.
43661 is the difference of 2 positive pentagonal numbers in 1 way.
43661 = 35² + 206² is the sum of 2 positive squares in 1 way.
43661 = 6² + 19² + 208² is the sum of 3 positive squares.
43661² = 14420² + 41211² is the sum of 2 positive squares in 1 way.
43661² is the sum of 3 positive squares.
43661 is a proper divisor of 1871³⁷ - 1.
43661 = '43' + '661' is the concatenation of 2 prime numbers.
43661 = '4' + '3661' is the concatenation of 2 semiprime numbers.
43661 is an emirp in (at least) the following bases: 5, 17, 19, 25, 27, 30, 35, 37, 49, 51, 56, 59, 61, 62, 63, 68, 73, 76, 86, 91, 97, and 99.

The number 43661 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024861: a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = (natural numbers), t = (F(2), F(3), F(4), ... ).
A141025: a(n) = (2^(2+n)-(-1)^n)/3 - 2*n.
A176616: Primes of the form x^2 + 7*y^2, where x and y=x+1 are consecutive natural numbers.
A211061: Number of 2 X 2 matrices having all terms in {1,...,n} and determinant >= n.
A222006: Number of forests of rooted plane binary trees (all nodes have outdegree of 0 or 2) with n total nodes.
A230087: Primes such that prime plus its digit sum is a perfect square.
A253394: Number of (n+1)X(5+1) 0..1 arrays with every 2X2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically
A272747: Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 529", based on the 5-celled von Neumann neighborhood.
A285790: Primes equal to a hexagonal number plus 1.
A285812: Primes equal to a centered 9-gonal number plus 1.

Number of the day: 75676125525

Properties of the number 75676125525:

75676125525 = 3 × 5² × 7² × 11² × 13² × 19 × 53 is composite and not squarefree.
75676125525 has 7 distinct prime factors, 648 divisors, 655 antidivisors and 26983756800 totatives.
75676125525 has an emirpimes digit sum 51 in base 10.
Reversing the decimal digits of 75676125525 results in a sphenic number.
75676125525 is the difference of 2 nonnegative squares in 324 ways.
75676125525 is the sum of 2 positive triangular numbers.
75676125525 is the difference of 2 positive pentagonal numbers in 132 ways.
75676125525 = 10² + 719² + 275092² is the sum of 3 positive squares.
75676125525² = 45405675315² + 60540900420² = 27414747360² + 70535860395² = 6568116555² + 75390555240² = 52435097715² + 54565891380² = 18627969360² + 73347629355² = 22933490580² + 72117480435² = 38420186805² + 65197892760² = 35059244220² + 67065083085² = 1823256435² + 75654158580² = 48906868395² + 57749408640² = 11015578035² + 74870107620² = 30201169845² + 69388509960² = 48421905840² + 58156642005² = 10388675220² + 74959665165² = 30780759240² + 69133355445² = 43933890000² + 61617280725² = 29106202125² + 69854885100² = 12191654475² + 74687613000² = 39979839900² + 64253314125² = 53286739275² + 53734527000² = 17472170100² + 73631509875² = 16855405875² + 73775139900² = 50488826388² + 56371574259² = 21189315147² + 72649080504² = 20389718349² + 72877536732² = 46851100296² + 59429373003² = 8382586212² + 75210426291² = 32616519936² + 68286445227² = 47501321868² + 58910953101² = 24923695797² + 71454078696² = 9208543344² + 75113771733² = 36838228812² + 66104620659² = 36664858923² + 66200937264² = 3843539469² + 75578457108² = 37390106061² + 65794041852² = 36109602144² + 66505432917² = 4475849532² + 75543647949² is the sum of 2 positive squares in 37 ways.
75676125525² is the sum of 3 positive squares.
75676125525 is a proper divisor of 1451¹⁵⁶ - 1.

Number of the day: 48609

Properties of the number 48609:

48609 = 3² × 11 × 491 is the 43609^th composite number and is not squarefree.
48609 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 29400 totatives.
48609 = 6³ + 25³ + 32³ is the sum of 3 positive cubes in 1 way.
48609 = (46 × 47)/2 + … + (72 × 73)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
48609 = 24305² - 24304² = 8103² - 8100² = 2705² - 2696² = 2215² - 2204² = 753² - 720² = 295² - 196² is the difference of 2 nonnegative squares in 6 ways.
48609 is the difference of 2 positive pentagonal numbers in 1 way.
48609 = 53² + 58² + 206² is the sum of 3 positive squares.
48609² is the sum of 3 positive squares.
48609 is a proper divisor of 881¹⁰ - 1.
48609 is palindromic in (at least) the following bases: 32, 72, and -75.
48609 in base 32 = 1ff1 and consists of only the digits '1' and 'f'.

The number 48609 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A158676: 62*n^2 + 1.
A289919: p-INVERT of (1,0,0,1,0,0,1,0,0,...), where p(S) = (1 - S)^2.

Number of the day: 7222018

Happy Casual π Day!

Properties of the number 7222018:

7222018 = 2 × 727 × 4967 is a sphenic number and squarefree.
7222018 has 3 distinct prime factors, 8 divisors, 27 antidivisors and 3605316 totatives.
7222018 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 7222018 results in a sphenic number.
7222018 is the difference of 2 positive pentagonal numbers in 3 ways.
7222018 = 57² + 412² + 2655² is the sum of 3 positive squares.
7222018² is the sum of 3 positive squares.
7222018 is a proper divisor of 1453⁴⁹⁶⁶ - 1.

Number of the day: 419938

Properties of the number 419938:

419938 = 2 × 19 × 43 × 257 is the 384550^th composite number and is squarefree.
419938 has 4 distinct prime factors, 16 divisors, 19 antidivisors and 193536 totatives.
419938 has a semiprime digit sum 34 in base 10.
419938 has a Fibonacci digit sum 34 in base 10.
419938 is the sum of 2 positive triangular numbers.
419938 is the difference of 2 positive pentagonal numbers in 6 ways.
419938 = 49² + 96² + 639² is the sum of 3 positive squares.
419938² = 52288² + 416670² is the sum of 2 positive squares in 1 way.
419938² is the sum of 3 positive squares.
419938 is a proper divisor of 1543⁶³ - 1.
419938 is palindromic in (at least) base -92.

Number of the day: 9437019

Properties of the number 9437019:

9437019 is a cyclic number.
9437019 = 3 × 3145673 is semiprime and squarefree.
9437019 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 6291344 totatives.
9437019 has a semiprime digit sum 33 in base 10.
Reversing the decimal digits of 9437019 results in a sphenic number.
9437019 = 4718510² - 4718509² = 1572838² - 1572835² is the difference of 2 nonnegative squares in 2 ways.
9437019 is the difference of 2 positive pentagonal numbers in 1 way.
9437019 = 137² + 155² + 3065² is the sum of 3 positive squares.
9437019² = 6585144² + 6759675² is the sum of 2 positive squares in 1 way.
9437019² is the sum of 3 positive squares.
9437019 is a proper divisor of 199³⁹³²⁰⁹ - 1.
9437019 is an emirpimes in (at least) the following bases: 3, 6, 9, 12, 21, 30, 36, 45, 50, 54, 55, 65, 69, 75, 78, and 96.

Number of the day: 91941997592

Properties of the number 91941997592:

91941997592 = 2³ × 48991 × 234589 is composite and not squarefree.
91941997592 has 3 distinct prime factors, 16 divisors, 79 antidivisors and 45969864480 totatives.
91941997592 has a semiprime digit sum 65 in base 10.
Reversing the decimal digits of 91941997592 results in a semiprime.
91941997592 = 22985499399² - 22985499397² = 11492749701² - 11492749697² = 518169² - 420187² = 332571² - 136607² is the difference of 2 nonnegative squares in 4 ways.
91941997592 = 2082² + 2492² + 303202² is the sum of 3 positive squares.
91941997592² = 43104241440² + 81211792808² is the sum of 2 positive squares in 1 way.
91941997592² is the sum of 3 positive squares.
91941997592 is a proper divisor of 311^1798508 - 1.

Number of the day: 7172018

Happy Yellow Pig Day!

Properties of the number 7172018:

7172018 = 2 × 7 × 512287 is a sphenic number and squarefree.
7172018 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 3073716 totatives.
7172018 has an emirpimes digit sum 26 in base 10.
Reversing the decimal digits of 7172018 results in a semiprime.
7172018 = 8² + 75² + 2677² is the sum of 3 positive squares.
7172018² is the sum of 3 positive squares.
7172018 is a proper divisor of 71⁸⁵³⁸¹ - 1.
7172018 = '717' + '2018' is the concatenation of 2 semiprime numbers.

Number of the day: 346

Properties of the number 346:

346 = 2 × 173 is semiprime and squarefree.
346 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 172 totatives.
346 has an emirp digit sum 13 in base 10.
346 has a Fibonacci digit sum 13 in base 10.
346 has an oblong digit product 72 in base 10.
Reversing the decimal digits of 346 results in a prime.
346 is the sum of 2 positive triangular numbers.
346 is the difference of 2 positive pentagonal numbers in 2 ways.
346 = 11² + 15² is the sum of 2 positive squares in 1 way.
346 = 3² + 9² + 16² is the sum of 3 positive squares.
346² = 104² + 330² is the sum of 2 positive squares in 1 way.
346² is the sum of 3 positive squares.
346 is a proper divisor of 691² - 1.
346 = '34' + '6' is the concatenation of 2 semiprime numbers.
346 is an emirpimes in (at least) the following bases: 3, 11, 13, 14, 16, 18, 19, 21, 23, 24, 25, 26, 29, 31, 32, 33, 34, 35, 38, 41, 43, 44, 45, 46, 50, 52, 55, 56, 68, 69, 71, 73, 79, 85, 89, 90, 91, 92, and 94.
346 is palindromic in (at least) the following bases: 9, 15, -23, and -69.
346 in base 4 = 11122 and consists of only the digits '1' and '2'.
346 in base 9 = 424 and consists of only the digits '2' and '4'.
346 in base 14 = 1aa and consists of only the digits '1' and 'a'.
346 in base 15 = 181 and consists of only the digits '1' and '8'.
346 in base 18 = 114 and consists of only the digits '1' and '4'.

The number 346 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000172: Franel number a(n) = Sum_{k = 0..n} binomial(n,k)^3.
A004207: a(0) = 1, a(n) = sum of digits of all previous terms.
A006753: Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).
A007811: Numbers n for which 10n+1, 10n+3, 10n+7 and 10n+9 are primes.
A100484: Even semiprimes.
A143164: Numbers with digitsum 13, in increasing order.
A161344: Numbers n with A033676(n)=2, where A033676 is the largest divisor <= sqrt(n).
A259934: Infinite sequence starting with a(0)=0 such that A049820(a(k)) = a(k-1) for all k>=1, where A049820(n) = n - (number of divisors of n).
A301678: Coordination sequence for node of type V1 in "krn" 2-D tiling (or net).
A301712: Coordination sequence for node of type V1 in "usm" 2-D tiling (or net).

Number of the day: 6143

Properties of the number 6143:

6143 is a cyclic number.
6143 is the 801^th prime.
6143 has 33 antidivisors and 6142 totatives.
6143 has a semiprime digit sum 14 in base 10.
6143 has an oblong digit product 72 in base 10.
6143 = 3072² - 3071² is the difference of 2 nonnegative squares in 1 way.
6143 is the difference of 2 positive pentagonal numbers in 1 way.
6143 is not the sum of 3 positive squares.
6143² is the sum of 3 positive squares.
6143 is a proper divisor of 409³⁷ - 1.
6143 = '61' + '43' is the concatenation of 2 prime numbers.
6143 = '6' + '143' is the concatenation of 2 semiprime numbers.
6143 is an emirp in (at least) the following bases: 7, 13, 15, 16, 17, 26, 37, 44, 49, 57, 58, 65, 66, 69, 76, 79, 83, 84, 85, 86, 88, 91, 94, 97, and 99.
6143 is palindromic in (at least) the following bases: 33, 74, -69, and -83.
6143 in base 4 = 1133333 and consists of only the digits '1' and '3'.
6143 in base 32 = 5vv and consists of only the digits '5' and 'v'.
6143 in base 33 = 5l5 and consists of only the digits '5' and 'l'.

The number 6143 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005105: Class 1+ primes: primes of the form 2^i*3^j - 1 with i, j >= 0.
A045712: Primes with first digit 6.
A052955: a(2n) = 2*2^n - 1, a(2n+1) = 3*2^n - 1.
A055010: a(0) = 0; for n > 0, a(n) = 3*2^(n-1) - 1.
A061712: Smallest prime with Hamming weight n (i.e., with exactly n 1's when written in binary).
A083329: a(0) = 1; for n > 0, a(n) = 3*2^(n-1) - 1.
A113156: Primes such that the sum of the predecessor and successor primes is divisible by 37.
A127581: Smallest prime of the form k*2^n - 1, for k >= 2.
A141908: Primes congruent to 2 mod 23.
A153893: a(n) = 3*2^n - 1.

Number of the day: 998423264023

Properties of the number 998423264023:

998423264023 is a cyclic number.
998423264023 = 311 × 1193 × 2691001 is a sphenic number and squarefree.
998423264023 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 994378320000 totatives.
Reversing the decimal digits of 998423264023 results in a sphenic number.
998423264023 = 499211632012² - 499211632011² = 1605182252² - 1605181941² = 418451252² - 418450059² = 1531012² - 1159989² is the difference of 2 nonnegative squares in 4 ways.
998423264023 is the difference of 2 positive pentagonal numbers in 4 ways.
998423264023 is not the sum of 3 positive squares.
998423264023² = 620691797160² + 782042650423² = 127603429065² + 990235516952² = 100559931752² + 993346220745² = 696301890752² + 715550620905² is the sum of 2 positive squares in 4 ways.
998423264023² is the sum of 3 positive squares.
998423264023 is a proper divisor of 347^15421500 - 1.

Number of the day: 4847

Properties of the number 4847:

4847 is a cyclic number.
4847 = 37 × 131 is semiprime and squarefree.
4847 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 4680 totatives.
4847 has a prime digit sum 23 in base 10.
4847 = 2424² - 2423² = 84² - 47² is the difference of 2 nonnegative squares in 2 ways.
4847 is the difference of 2 positive pentagonal numbers in 1 way.
4847 is not the sum of 3 positive squares.
4847² = 1572² + 4585² is the sum of 2 positive squares in 1 way.
4847² is the sum of 3 positive squares.
4847 is a proper divisor of 787³ - 1.
4847 is an emirpimes in (at least) the following bases: 2, 5, 7, 13, 16, 17, 22, 23, 27, 28, 33, 39, 45, 49, 50, 51, 52, 55, 57, 62, 64, 65, 66, 68, 69, 71, 73, 75, 81, 86, 88, 94, 96, and 97.
4847 is palindromic in (at least) the following bases: -51, and -57.

The number 4847 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A015882: Numbers n such that sigma(n) = sigma(n + 12).
A024784: Every suffix prime and no 0 digits in base 9 (written in base 9).
A061722: a(n) = 10 * n^2 + 7.
A064699: Integers for which the smallest m in A040076 such that n*2^m+1 is prime (A050921) increases.
A140689: a(n) = n*(3*n + 20).
A152527: a(n) = (p(n)*p(n+1)-p(n+2))/2, where p(n) is the n-th odd prime.
A186029: a(n) = n*(7*n+3)/2.
A218569: Number of partitions p of n such that max(p)-min(p) = 6.
A235039: Odd numbers which are factored to the same set of primes in Z as to the irreducible polynomials in GF(2)[X]; odd terms of A235036.
A281525: Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 374", based on the 5-celled von Neumann neighborhood.

Number of the day: 5981

Properties of the number 5981:

5981 is a cyclic number.
5981 is the 782^th prime.
5981 has 9 antidivisors and 5980 totatives.
5981 has a prime digit sum 23 in base 10.
5981 has sum of divisors equal to 5982 which is a sphenic number.
Reversing the decimal digits of 5981 results in a semiprime.
5981 = 2991² - 2990² is the difference of 2 nonnegative squares in 1 way.
5981 is the difference of 2 positive pentagonal numbers in 1 way.
5981 = 50² + 59² is the sum of 2 positive squares in 1 way.
5981 = 11² + 26² + 72² is the sum of 3 positive squares.
5981² = 981² + 5900² is the sum of 2 positive squares in 1 way.
5981² is the sum of 3 positive squares.
5981 is a proper divisor of 1433⁵ - 1.
5981 is an emirp in (at least) the following bases: 4, 9, 21, 23, 34, 40, 43, 51, 57, 61, 64, 66, 72, 77, 81, 83, 84, 86, 88, 89, 92, 95, and 97.
5981 is palindromic in (at least) the following bases: 2, 29, 65, -36, -43, -49, and -92.
5981 in base 4 = 1131131 and consists of only the digits '1' and '3'.
5981 in base 28 = 7hh and consists of only the digits '7' and 'h'.
5981 in base 29 = 737 and consists of only the digits '3' and '7'.
5981 in base 31 = 66t and consists of only the digits '6' and 't'.
5981 in base 34 = 55v and consists of only the digits '5' and 'v'.
5981 in base 44 = 33f and consists of only the digits '3' and 'f'.
5981 in base 54 = 22f and consists of only the digits '2' and 'f'.

The number 5981 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A016041: Primes that are palindromic in base 2 (but written here in base 10).
A040984: Primes p such that x^23 = 2 has no solution mod p.
A077323: Final terms of rows of A077321.
A127340: Primes that are the sum of 11 consecutive primes.
A136065: Mother primes of order 6.
A141779: Numbers n such that A120292(n) is composite.
A142508: Primes congruent to 1 mod 52.
A154616: Primes of the form (4*n^2-8*n-9)/3.
A158712: Primes p such that p1=Floor[p/2]+p is prime and p2=Ceiling[p1/2]+p is prime.
A215560: a(n) = 3*a(n-1) + 46*a(n-2) + a(n-3) with a(0)=a(1)=3, a(2)=101.

Number of the day: 592497

Properties of the number 592497:

592497 = 3² × 43 × 1531 is the 543967^th composite number and is not squarefree.
592497 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 385560 totatives.
592497 has a triangular digit sum 36 in base 10.
592497 = 296249² - 296248² = 98751² - 98748² = 32921² - 32912² = 6911² - 6868² = 2361² - 2232² = 959² - 572² is the difference of 2 nonnegative squares in 6 ways.
592497 is the difference of 2 positive pentagonal numbers in 2 ways.
592497 = 29² + 70² + 766² is the sum of 3 positive squares.
592497² is the sum of 3 positive squares.
592497 is a proper divisor of 647⁴² - 1.

Number of the day: 635333602007111

Properties of the number 635333602007111:

635333602007111 = 7 × 43 × 67 × 571 × 1901 × 29023 is composite and squarefree.
635333602007111 has 6 distinct prime factors, 64 divisors, 131 antidivisors and 522757498032000 totatives.
635333602007111 has a prime digit sum 41 in base 10.
635333602007111 is the difference of 2 nonnegative squares in 32 ways.
635333602007111 is the difference of 2 positive pentagonal numbers in 29 ways.
635333602007111 is not the sum of 3 positive squares.
635333602007111² = 183481403209839² + 608262575304020² is the sum of 2 positive squares in 1 way.
635333602007111² is the sum of 3 positive squares.
635333602007111 is a proper divisor of 677^1596210 - 1.
635333602007111 = '6' + '35333602007111' is the concatenation of 2 semiprime numbers.

Number of the day: 12602

Properties of the number 12602:

12602 = 2 × 6301 is semiprime and squarefree.
12602 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 6300 totatives.
12602 has a prime digit sum 11 in base 10.
12602 has sum of divisors equal to 18906 which is an oblong number.
Reversing the decimal digits of 12602 results in an emirpimes.
12602 = 49² + 101² is the sum of 2 positive squares in 1 way.
12602 = 5² + 16² + 111² is the sum of 3 positive squares.
12602² = 7800² + 9898² is the sum of 2 positive squares in 1 way.
12602² is the sum of 3 positive squares.
12602 is a proper divisor of 271¹⁰ - 1.
12602 = '1260' + '2' is the concatenation of 2 oblong numbers.
12602 is an emirpimes in (at least) the following bases: 6, 9, 10, 11, 16, 18, 19, 20, 21, 22, 27, 30, 31, 37, 39, 40, 42, 43, 44, 50, 55, 58, 59, 60, 62, 64, 66, 67, 69, 73, 74, 77, 81, 82, 84, 85, 86, 88, 90, 91, 94, 97, 99, and 100.
12602 is palindromic in (at least) the following bases: 26, 70, 72, 75, -47, -51, -84, -90, and -100.
12602 in base 18 = 22g2 and consists of only the digits '2' and 'g'.
12602 in base 24 = ll2 and consists of only the digits '2' and 'l'.
12602 in base 26 = igi and consists of only the digits 'g' and 'i'.
12602 in base 28 = g22 and consists of only the digits '2' and 'g'.
12602 in base 35 = aa2 and consists of only the digits '2' and 'a'.
12602 in base 50 = 522 and consists of only the digits '2' and '5'.

The number 12602 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005905: Number of points on surface of truncated tetrahedron: 14n^2 + 2 for n>0, a(0)=1.
A094616: Row sums of A094615.
A100195: Numbers n such that the denominator of BernoulliB(n) is a record.
A129210: Largest number not the sum of n distinct nonzero squares.
A132174: Index of starting position of n-th generation of terms in A063882.
A154335: A triangular sequence of coefficients of polynomials: p(x,n) = (2*(x - 1)^n * (Sum_{k>=0} (((-1)^n*(2*k + 1)^(n - 1)))*x^k) - (x - 1)^(n + 1)*(Sum_{k>=0} ((-1)^(n + 1)*k^n)*x^k)/x).
A261621: Rocket Sequence 42: a(0) = 42, a(n) = A073846(a(n-1)).
A263097: First differences of A263096.
A273366: a(n) = 10*n^2 + 10*n + 2.
A299285: Coordination sequence for "tea" 3D uniform tiling.

Number of the day: 3945755420

Properties of the number 3945755420:

3945755420 = 2² × 5 × 17 × 71 × 149 × 1097 is the 3758248020^th composite number and is not squarefree.
3945755420 has 6 distinct prime factors, 96 divisors, 47 antidivisors and 1453383680 totatives.
3945755420 is the difference of 2 nonnegative squares in 16 ways.
3945755420 is the difference of 2 positive pentagonal numbers in 14 ways.
3945755420 is not the sum of 3 positive squares.
3945755420² = 2367453252² + 3156604336² = 1144004256² + 3776273308² = 2155600612² + 3304901184² = 1671143472² + 3574390204² = 346752924² + 3930489568² = 2786485312² + 2793650916² = 767654272² + 3870360804² = 603468476² + 3899334768² = 1901688992² + 3457248156² = 2132557136² + 3319817148² = 867431708² + 3849226944² = 2389355616² + 3140058212² = 1046019996² + 3804579872² = 319401168² + 3932806724² = 1646236956² + 3585929408² = 1568908016² + 3620430012² = 234934172² + 3938755104² = 2713349348² + 2864737536² = 2589908464² + 2976803652² = 1414565092² + 3683475456² = 1910517984² + 3452376988² = 1407811004² + 3686062128² = 61103168² + 3945282276² = 2584447712² + 2981545884² = 877314624² + 3846986468² = 492431292² + 3914907056² = 1802688864² + 3509885852² = 2104163100² + 3337886080² = 834568080² + 3856485700² = 2416051900² + 3119563920² = 1954999200² + 3427384420² = 663780420² + 3889522000² = 2551200400² + 3010043580² = 1078433200² + 3795519420² = 285844580² + 3935388000² = 1615590800² + 3599840580² = 1856826080² + 3481548900² = 552997700² + 3906811920² = 2635696080² + 2936339900² = 1350560580² + 3707421200² is the sum of 2 positive squares in 40 ways.
3945755420² is the sum of 3 positive squares.
3945755420 is a proper divisor of 1789⁵⁴⁸⁰ - 1.

Number of the day: 406031

Properties of the number 406031:

406031 is a cyclic number.
406031 = 173 × 2347 is semiprime and squarefree.
406031 has 2 distinct prime factors, 4 divisors, 15 antidivisors and 403512 totatives.
406031 has a semiprime digit sum 14 in base 10.
406031 = 203016² - 203015² = 1260² - 1087² is the difference of 2 nonnegative squares in 2 ways.
406031 is the difference of 2 positive pentagonal numbers in 2 ways.
406031 is not the sum of 3 positive squares.
406031² = 122044² + 387255² is the sum of 2 positive squares in 1 way.
406031² is the sum of 3 positive squares.
406031 is a proper divisor of 1063²⁵⁸ - 1.
406031 is an emirpimes in (at least) the following bases: 2, 4, 5, 6, 7, 20, 22, 24, 26, 27, 31, 35, 40, 43, 58, 59, 60, 62, 64, 68, 69, 70, 71, 74, 79, 80, 85, 93, and 95.
406031 is palindromic in (at least) the following bases: 94, and -38.

Number of the day: 49126

Properties of the number 49126:

49126 = 2 × 7 × 11² × 29 is the 44075^th composite number and is not squarefree.
49126 has 4 distinct prime factors, 24 divisors, 19 antidivisors and 18480 totatives.
49126 has a semiprime digit sum 22 in base 10.
49126 is the sum of 2 positive triangular numbers.
49126 is the difference of 2 positive pentagonal numbers in 5 ways.
49126 = 6² + 79² + 207² is the sum of 3 positive squares.
49126² = 33880² + 35574² is the sum of 2 positive squares in 1 way.
49126² is the sum of 3 positive squares.
49126 is a proper divisor of 1451⁶ - 1.
49126 is palindromic in (at least) the following bases: -42, -48, and -82.
49126 in base 47 = MBB and consists of only the digits 'B' and 'M'.

The number 49126 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A204554: Permanent of the n-th principal submatrix of A204553.
A208838: Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically
A208840: T(n,k)=Number of nXk 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically
A208842: Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically

Number of the day: 414955

Properties of the number 414955:

414955 is a cyclic number.
414955 = 5 × 37 × 2243 is a sphenic number and squarefree.
414955 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 322848 totatives.
414955 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 414955 results in a semiprime.
414955 = 207478² - 207477² = 41498² - 41493² = 5626² - 5589² = 1214² - 1029² is the difference of 2 nonnegative squares in 4 ways.
414955 is the difference of 2 positive pentagonal numbers in 4 ways.
414955 = 117² + 125² + 621² is the sum of 3 positive squares.
414955² = 248973² + 331964² = 233272² + 343179² = 127851² + 394768² = 134580² + 392525² is the sum of 2 positive squares in 4 ways.
414955² is the sum of 3 positive squares.
414955 is a proper divisor of 433²²⁸ - 1.
414955 is palindromic in (at least) base 76.