Number of the day: 12350

Carl Friedrich Gauss was born on this day 239 years ago.

Claude Shannon was born on this day 100 years ago.

Properties of the number 12350:

12350 = 2 × 5² × 13 × 19 is the 10874^th composite number and is not squarefree.
12350 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 4320 totatives.
12350 has a prime digit sum 11 in base 10.
12350 is the difference of 2 positive pentagonal numbers in 3 ways.
12350 = 2² + 5² + 111² is the sum of 3 positive squares.
12350² = 7410² + 9880² = 3040² + 11970² = 6270² + 10640² = 4750² + 11400² = 3458² + 11856² = 1368² + 12274² = 7752² + 9614² is the sum of 2 positive squares in 7 ways.
12350² is the sum of 3 positive squares.
12350 is a divisor of 1901³ - 1.
12350 is palindromic in (at least) the following bases: 18, and 31.
12350 in base 18 = 2222 and consists of only the digit '2'.
12350 in base 25 = jj0 and consists of only the digits '0' and 'j'.
12350 in base 31 = cqc and consists of only the digits 'c' and 'q'.
12350 in base 33 = bb8 and consists of only the digits '8' and 'b'.
12350 in base 55 = 44U and consists of only the digits '4' and 'U'.

The number 12350 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005587: n(n+5)(n+6)(n+7)/24.
A024868: a(n) = 2*(n+1) + 3*n + ... + (k+1)*(n+2-k), where k = [ n/2 ].
A029774: Digits of n^2 appear in n.
A035615: Number of winning length n strings with a 2 symbol alphabet in "same game".
A102150: a(0)=0; a(1)=2. Slowest increasing sequence where every digit "d" has a copy of itself in a(n+d).
A114166: Numbers n such that p(5n) is prime, where p(n) is the number of partitions of n.
A143554: G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^4.
A181373: Least m>0 such that prime(n) divides S(m)=A007908(m)=123...m and all numbers obtained by cyclic permutations of its digits; 0 if no such m exists.
A211183: Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 1, 3, 3, 6, 6, 10, 10, 15, ...) DELTA (1, 0, 2, 0, 3, 0, 4, 0, 5, ...) where DELTA is the operator defined in A084938.
A234508: 5*binomial(9*n+5,n)/(9*n+5).

Number of the day: 289869

Henri Poincaré was born on this day 162 years ago.

Properties of the number 289869:

289869 = 3 × 23 × 4201 is a sphenic number and squarefree.
289869 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 184800 totatives.
289869 has a sphenic digit sum 42 in base 10.
289869 has an oblong digit sum 42 in base 10.
289869 = 144935² - 144934² = 48313² - 48310² = 6313² - 6290² = 2135² - 2066² is the difference of 2 nonnegative squares in 4 ways.
289869 is the difference of 2 positive pentagonal numbers in 2 ways.
289869 = 35² + 88² + 530² is the sum of 3 positive squares.
289869² = 69069² + 281520² is the sum of 2 positive squares in 1 way.
289869² is the sum of 3 positive squares.
289869 is a divisor of 1013¹² - 1.
289869 = '289' + '869' is the concatenation of 2 semiprime numbers.

Number of the day: 1718

Kurt Gödel was born on this day 110 years ago.

Properties of the number 1718:

1718 = 2 × 859 is semiprime and squarefree.
1718 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 858 totatives.
1718 has an emirp digit sum 17 in base 10.
1718 has an oblong digit product 56 in base 10.
Reversing the decimal digits of 1718 results in a prime.
1718 = 1² + 6² + 41² is the sum of 3 positive squares.
1718² is the sum of 3 positive squares.
1718 is a divisor of 599⁶ - 1.
1718 is an emirpimes in (at least) the following bases: 4, 5, 9, 15, 17, 19, 25, 31, 34, 35, 36, 37, 38, 39, 40, 45, 50, 53, 54, 55, 58, 64, 66, 67, 71, 72, 74, 76, 78, 79, 83, 87, 92, 94, 95, 99, and 100.
1718 is palindromic in (at least) the following bases: 16, and 26.
1718 in base 5 = 23333 and consists of only the digits '2' and '3'.
1718 in base 12 = bb2 and consists of only the digits '2' and 'b'.
1718 in base 13 = a22 and consists of only the digits '2' and 'a'.
1718 in base 14 = 8aa and consists of only the digits '8' and 'a'.
1718 in base 16 = 6b6 and consists of only the digits '6' and 'b'.
1718 in base 18 = 558 and consists of only the digits '5' and '8'.
1718 in base 25 = 2ii and consists of only the digits '2' and 'i'.
1718 in base 26 = 2e2 and consists of only the digits '2' and 'e'.

The number 1718 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000954: Conjecturally largest even integer which is an unordered sum of two primes in exactly n ways.
A001704: a(n) = concatenation {n,n+1}.
A056045: a(n) = Sum_{k|n} binomial(n,k).
A071148: Partial sums of sequence of odd primes [A065091]; a(n) = sum of the first n odd primes.
A077295: Partition the concatenation 1234567...of natural numbers into successive strings which are even, all different and > 2. (0's never taken as the most significant digit.)
A112816: Numbers n such that 9*LCM(1,2,3,...,n) equals the denominator of the n-th harmonic number H(n).
A159051: Numbers n such that Fibonacci(n-2) is divisible by n.
A160164: Number of toothpicks after n-th stage in the I-toothpick structure of A139250.
A183561: Number of partitions of n containing a clique of size 4.
A187705: T(n,k)=Number of (n+1)X(n+1) 0..k arrays with each 2X2 subblock off diagonal and antidiagonal nonsingular and the array of 2X2 subblock determinants antisymmetric about the diagonal and antidiagonal

Number of the day: 481648881540

Properties of the number 481648881540:

481648881540 = 2² × 3 × 5 × 43 × 186685613 is composite and not squarefree.
481648881540 has 5 distinct prime factors, 48 divisors, 23 antidivisors and 125452731264 totatives.
481648881540 has a semiprime digit sum 57 in base 10.
481648881540 = 120412220386² - 120412220384² = 40137406798² - 40137406792² = 24082444082² - 24082444072² = 8027481374² - 8027481344² = 2800284238² - 2800284152² = 933428194² - 933427936² = 560057054² - 560056624² = 186686258² - 186684968² is the difference of 2 nonnegative squares in 8 ways.
481648881540 is the sum of 2 positive triangular numbers.
481648881540 is the difference of 2 positive pentagonal numbers in 4 ways.
481648881540 = 682² + 2620² + 694004² is the sum of 3 positive squares.
481648881540² = 302422592736² + 374868270852² = 288989328924² + 385319105232² = 185362573188² + 444551865984² = 118441061040² + 466859036700² is the sum of 2 positive squares in 4 ways.
481648881540² is the sum of 3 positive squares.
481648881540 is a divisor of 431^93342806 - 1.

Number of the day: 807685

Properties of the number 807685:

807685 = 5 × 67 × 2411 is a sphenic number and squarefree.
807685 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 636240 totatives.
807685 has a semiprime digit sum 34 in base 10.
807685 has a Fibonacci digit sum 34 in base 10.
807685 = 403843² - 403842² = 80771² - 80766² = 6061² - 5994² = 1373² - 1038² is the difference of 2 nonnegative squares in 4 ways.
807685 is the difference of 2 positive pentagonal numbers in 4 ways.
807685 = 50² + 129² + 888² is the sum of 3 positive squares.
807685² = 484611² + 646148² is the sum of 2 positive squares in 1 way.
807685² is the sum of 3 positive squares.
807685 is a divisor of 13⁶⁶⁰ - 1.
807685 = '807' + '685' is the concatenation of 2 semiprime numbers.

Number of the day: 658225

Felix Klein was born on this day 167 years ago.

Andrey Kolmogorov was born on this day 113 years ago.

Properties of the number 658225:

658225 = 5² × 113 × 233 is the 604794^th composite number and is not squarefree.
658225 has 3 distinct prime factors, 12 divisors, 19 antidivisors and 519680 totatives.
658225 has a triangular digit sum 28 in base 10.
658225 = 13² + … + 125² is the sum of at least 2 consecutive positive squares in 1 way.
658225 = 329113² - 329112² = 65825² - 65820² = 13177² - 13152² = 2969² - 2856² = 1529² - 1296² = 865² - 300² is the difference of 2 nonnegative squares in 6 ways.
658225 is the sum of 2 positive triangular numbers.
658225 is the difference of 2 positive pentagonal numbers in 6 ways.
658225 = 240² + 775² = 135² + 800² = 476² + 657² = 372² + 721² = 559² + 588² = 273² + 764² is the sum of 2 positive squares in 6 ways.
658225 = 35² + 198² + 786² is the sum of 3 positive squares.
658225² = 321540² + 574345² = 28215² + 657620² = 367820² + 545865² = 216000² + 621775² = 87375² + 652400² = 372000² + 543025² = 266552² + 601839² = 33263² + 657384² = 417144² + 509167² = 461340² + 469495² = 200265² + 627020² = 211220² + 623415² = 205073² + 625464² = 98792² + 650769² = 381457² + 536424² = 394935² + 526580² = 115260² + 648055² = 292105² + 589860² = 296625² + 587600² = 184303² + 631896² = 120232² + 647151² = 449288² + 481041² is the sum of 2 positive squares in 22 ways.
658225² is the sum of 3 positive squares.
658225 is a divisor of 467²⁰ - 1.

Number of the day: 182420

Properties of the number 182420:

182420 = 2² × 5 × 7 × 1303 is the 165890^th composite number and is not squarefree.
182420 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 62496 totatives.
182420 has an emirp digit sum 17 in base 10.
182420 = 45606² - 45604² = 9126² - 9116² = 6522² - 6508² = 1338² - 1268² is the difference of 2 nonnegative squares in 4 ways.
182420 is the difference of 2 positive pentagonal numbers in 4 ways.
182420 = 12² + 50² + 424² is the sum of 3 positive squares.
182420² = 109452² + 145936² is the sum of 2 positive squares in 1 way.
182420² is the sum of 3 positive squares.
182420 is a divisor of 1399⁶ - 1.
182420 = '182' + '420' is the concatenation of 2 oblong numbers.
182420 is palindromic in (at least) the following bases: 12, and 95.

Number of the day: 241208551

Properties of the number 241208551:

241208551 = 31 × 7780921 is semiprime and squarefree.
241208551 has 2 distinct prime factors, 4 divisors, 25 antidivisors and 233427600 totatives.
241208551 has a triangular digit sum 28 in base 10.
Reversing the decimal digits of 241208551 results in an emirpimes.
241208551 = 120604276² - 120604275² = 3890476² - 3890445² is the difference of 2 nonnegative squares in 2 ways.
241208551 is the sum of 2 positive triangular numbers.
241208551 is the difference of 2 positive pentagonal numbers in 2 ways.
241208551 is not the sum of 3 positive squares.
241208551² = 112645351² + 213289920² is the sum of 2 positive squares in 1 way.
241208551² is the sum of 3 positive squares.
241208551 is a divisor of 1733²⁴⁷⁸⁰ - 1.
241208551 is an emirpimes in (at least) the following bases: 2, 3, 6, 8, 9, 10, 11, 15, 18, 19, 20, 21, 24, 29, 35, 37, 39, 40, 42, 51, 54, 61, 67, 68, 71, 80, 85, 87, 91, 95, and 97.

Number of the day: 32920

Properties of the number 32920:

32920 = 2³ × 5 × 823 is the 29391^th composite number and is not squarefree.
32920 has 3 distinct prime factors, 16 divisors, 9 antidivisors and 13152 totatives.
32920 = 38³ - 28³ is the difference of 2 positive cubes in 1 way.
32920 = 8231² - 8229² = 4117² - 4113² = 1651² - 1641² = 833² - 813² is the difference of 2 nonnegative squares in 4 ways.
32920 is the difference of 2 positive pentagonal numbers in 2 ways.
32920 = 12² + 50² + 174² is the sum of 3 positive squares.
32920² = 19752² + 26336² is the sum of 2 positive squares in 1 way.
32920² is the sum of 3 positive squares.
32920 is a divisor of 1471⁶ - 1.

The number 32920 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A154256: Coefficients of x^n in the (n-1)-th iterations of x*(1+x)^2 for n>=1.
A203543: Number of n X n 0..4 arrays with every nonzero element less than or equal to some NW, E or S neighbor
A203545: Number of nX3 0..4 arrays with every nonzero element less than or equal to some NW, E or S neighbor
A203550: T(n,k)=Number of nXk 0..4 arrays with every nonzero element less than or equal to some NW, E or S neighbor
A206198: Number of (n+1)X(n+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases
A206202: Number of (n+1)X5 0..3 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases
A206206: T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X3 or 3X2 subblock having exactly one clockwise edge increases

Number of the day: 64955

Properties of the number 64955:

64955 = 5 × 11 × 1181 is a sphenic number and squarefree.
64955 has 3 distinct prime factors, 8 divisors, 15 antidivisors and 47200 totatives.
64955 has a prime digit sum 29 in base 10.
Reversing the decimal digits of 64955 results in a sphenic number.
64955 = 32478² - 32477² = 6498² - 6493² = 2958² - 2947² = 618² - 563² is the difference of 2 nonnegative squares in 4 ways.
64955 is the difference of 2 positive pentagonal numbers in 4 ways.
64955 = 27² + 35² + 251² is the sum of 3 positive squares.
64955² = 38973² + 51964² = 38544² + 52283² = 22363² + 60984² = 18700² + 62205² is the sum of 2 positive squares in 4 ways.
64955² is the sum of 3 positive squares.
64955 is a divisor of 3²⁰ - 1.
64955 = '6' + '4955' is the concatenation of 2 semiprime numbers.

Number of the day: 506117

Properties of the number 506117:

506117 = 61 × 8297 is semiprime and squarefree.
506117 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 497760 totatives.
506117 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 506117 results in a sphenic number.
506117 = 253059² - 253058² = 4179² - 4118² is the difference of 2 nonnegative squares in 2 ways.
506117 is the difference of 2 positive pentagonal numbers in 2 ways.
506117 = 479² + 526² = 431² + 566² is the sum of 2 positive squares in 2 ways.
506117 = 9² + 44² + 710² is the sum of 3 positive squares.
506117² = 47235² + 503908² = 44408² + 504165² = 134595² + 487892² = 91267² + 497820² is the sum of 2 positive squares in 4 ways.
506117² is the sum of 3 positive squares.
506117 is a divisor of 479¹⁷⁰ - 1.
506117 is an emirpimes in (at least) the following bases: 3, 4, 8, 11, 14, 19, 24, 25, 26, 31, 32, 34, 37, 38, 40, 41, 43, 44, 46, 52, 53, 56, 59, 61, 65, 66, 67, 68, 72, 77, 79, 80, 82, 83, 85, 88, 91, and 94.
506117 is palindromic in (at least) base 89.

Number of the day: 5192

Properties of the number 5192:

5192 = 2³ × 11 × 59 is the 4500^th composite number and is not squarefree.
5192 has 3 distinct prime factors, 16 divisors, 11 antidivisors and 2320 totatives.
5192 has an emirp digit sum 17 in base 10.
5192 has an oblong digit product 90 in base 10.
Reversing the decimal digits of 5192 results in a sphenic number.
5192 = 1299² - 1297² = 651² - 647² = 129² - 107² = 81² - 37² is the difference of 2 nonnegative squares in 4 ways.
5192 is the difference of 2 positive pentagonal numbers in 1 way.
5192 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
5192 = (59 × (3 × 59-1))/2 is a pentagonal number.
5192 = 6² + 16² + 70² is the sum of 3 positive squares.
5192² is the sum of 3 positive squares.
5192 is a divisor of 353² - 1.
5192 = '51' + '92' is the concatenation of 2 pentagonal numbers.
5192 is palindromic in (at least) the following bases: 20, and 87.
5192 in base 20 = cjc and consists of only the digits 'c' and 'j'.
5192 in base 41 = 33Q and consists of only the digits '3' and 'Q'.

The number 5192 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033570: Pentagonal numbers with odd index: (2*n+1)*(3*n+1).
A035005: Number of possible queen moves on an n X n chessboard.
A035959: Number of partitions of n in which no parts are multiples of 5.
A057687: Trajectory of 29 under the `29x+1' map.
A105210: a(1) = 393; for n>1, a(n) = a(n-1) + 1 + sum of distinct prime factors of a(n-1) that are < a(n-1).
A116995: Pentagonal numbers with prime indices.
A136117: Pentagonal numbers (A000326) which are the sum of 2 other positive pentagonal numbers.
A152728: a(n)+a(n+1)+a(n+2)=n^3.
A252053: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum not 1 3 6 or 8 and every diagonal and antidiagonal sum 1 3 6 or 8
A270299: Numbers which are representable as a sum of eleven but no fewer consecutive nonnegative integers.

Number of the day: 69829139751575

Properties of the number 69829139751575:

69829139751575 = 5² × 17 × 107 × 1535550077 is composite and not squarefree.
69829139751575 has 4 distinct prime factors, 24 divisors, 87 antidivisors and 52085858577920 totatives.
69829139751575 has a semiprime digit sum 77 in base 10.
69829139751575 is the difference of 2 nonnegative squares in 12 ways.
69829139751575 is the difference of 2 positive pentagonal numbers in 12 ways.
69829139751575 is not the sum of 3 positive squares.
69829139751575² = 32860771647800² + 61613946839625² = 19127069376575² + 67158498907500² = 45116199197825² + 53297629669500² = 10679750785535² + 69007620460380² = 4114381556560² + 69707823254295² = 24993443843240² + 65203040751945² = 29574694483020² + 63256985422015² = 15568384216905² + 68071537159960² = 42250557500055² + 55596754845760² = 48798245896983² + 49948372904656² = 37166366295612² + 59116579525759² = 38533188707329² + 58234887537372² = 14294435666793² + 68350405027424² = 442393092588² + 69827738376641² = 28388214922452² + 63798260258111² = 41897483850945² + 55863311801260² = 29173344863880² + 63443082427465² = 45770474149015² + 52736822568480² = 14727173565375² + 68258472860300² = 19552159130441² + 67035974161512² = 4974285778124² + 69651742544193² = 33250459023644² + 61404525347583² is the sum of 2 positive squares in 22 ways.
69829139751575² is the sum of 3 positive squares.
69829139751575 is a divisor of 1277^4704286360 - 1.

Number of the day: 26672256451158

Properties of the number 26672256451158:

26672256451158 = 2 × 3 × 599 × 3539 × 2097013 is composite and squarefree.
26672256451158 has 5 distinct prime factors, 32 divisors, 35 antidivisors and 8873397233376 totatives.
26672256451158 is the difference of 2 positive pentagonal numbers in 4 ways.
26672256451158 = 3530² + 7033² + 5164513² is the sum of 3 positive squares.
26672256451158² = 11314397711130² + 24153543604008² is the sum of 2 positive squares in 1 way.
26672256451158² is the sum of 3 positive squares.
26672256451158 is a divisor of 977^2942107836 - 1.
26672256451158 = '266722' + '56451158' is the concatenation of 2 sphenic numbers.

Number of the day: 12501045020

Properties of the number 12501045020:

12501045020 = 2² × 5 × 89 × 7023059 is composite and not squarefree.
12501045020 has 4 distinct prime factors, 24 divisors, 15 antidivisors and 4944232832 totatives.
12501045020 has an oblong digit sum 20 in base 10.
12501045020 = 3125261256² - 3125261254² = 625052256² - 625052246² = 35115384² - 35115206² = 7023504² - 7022614² is the difference of 2 nonnegative squares in 4 ways.
12501045020 is the sum of 2 positive triangular numbers.
12501045020 is the difference of 2 positive pentagonal numbers in 4 ways.
12501045020 is not the sum of 3 positive squares.
12501045020² = 5477986020² + 11236894400² = 2359747824² + 12276307132² = 5702723908² + 11124525456² = 7500627012² + 10000836016² is the sum of 2 positive squares in 4 ways.
12501045020² is the sum of 3 positive squares.
12501045020 is a divisor of 101^4013176 - 1.

Number of the day: 4229

Leonhard Euler was born on this day 309 years ago.

Properties of the number 4229:

4229 and 4231 form a twin prime pair.
4229 has 5 antidivisors and 4228 totatives.
4229 has an emirp digit sum 17 in base 10.
4229 has a Fibonacci digit product 144 in base 10.
4229 = 2115² - 2114² is the difference of 2 nonnegative squares in 1 way.
4229 is the difference of 2 positive pentagonal numbers in 1 way.
4229 = 2² + 65² is the sum of 2 positive squares in 1 way.
4229 = 2² + 33² + 56² is the sum of 3 positive squares.
4229² = 260² + 4221² is the sum of 2 positive squares in 1 way.
4229² is the sum of 3 positive squares.
4229 is a divisor of 1213²⁸ - 1.
4229 = '422' + '9' is the concatenation of 2 semiprime numbers.
4229 is an emirp in (at least) the following bases: 2, 7, 9, 11, 18, 23, 24, 28, 37, 41, 45, 46, 48, 50, 51, 55, 56, 57, 65, 67, 73, 76, 77, 79, 81, 83, 92, and 97.
4229 is palindromic in (at least) base 19.
4229 in base 19 = bdb and consists of only the digits 'b' and 'd'.
4229 in base 26 = 66h and consists of only the digits '6' and 'h'.
4229 in base 32 = 445 and consists of only the digits '4' and '5'.
4229 in base 37 = 33B and consists of only the digits '3' and 'B'.

The number 4229 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A005473: Primes of form n^2 + 4.
A015523: a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=0, a(1)=1.
A078370: 4*(n+1)*n + 5.
A084740: Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists.
A089392: Magnanimous primes: primes with the property that inserting a "+" in any place between two digits yields a sum which is prime.
A113228: a(n) is the number of permutations of [1..n] that avoid the consecutive pattern 1324 (equally, the number that avoid 4231).
A174913: Lesser of twin primes p1 such that 2*p1+p2 is a prime number.
A175965: Lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.
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.
A264173: Number T(n,k) of permutations of [n] with exactly k (possibly overlapping) occurrences of the consecutive pattern 1324; triangle T(n,k), n>=0, 0<=k<=max(0,floor(n/2-1)), read by rows.

Number of the day: 348588115

Properties of the number 348588115:

348588115 = 5 × 23 × 3031201 is a sphenic number and squarefree.
348588115 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 266745600 totatives.
348588115 has a prime digit sum 43 in base 10.
Reversing the decimal digits of 348588115 results in a sphenic number.
348588115 = 174294058² - 174294057² = 34858814² - 34858809² = 7578014² - 7577991² = 1515658² - 1515543² is the difference of 2 nonnegative squares in 4 ways.
348588115 is the sum of 2 positive triangular numbers.
348588115 is the difference of 2 positive pentagonal numbers in 4 ways.
348588115 = 77² + 225² + 18669² is the sum of 3 positive squares.
348588115² = 182803885² + 296810400² = 31843132² + 347130651² = 127765989² + 324329348² = 209152869² + 278870492² is the sum of 2 positive squares in 4 ways.
348588115² is the sum of 3 positive squares.
348588115 is a divisor of 647⁶⁶⁰ - 1.
348588115 = '34858' + '8115' is the concatenation of 2 sphenic numbers.

Number of the day: 24576633

Properties of the number 24576633:

24576633 = 3² × 19 × 101 × 1423 is composite and not squarefree.
24576633 has 4 distinct prime factors, 24 divisors, 37 antidivisors and 15357600 totatives.
24576633 has a triangular digit sum 36 in base 10.
24576633 is the difference of 2 nonnegative squares in 12 ways.
24576633 is the sum of 2 positive triangular numbers.
24576633 is the difference of 2 positive pentagonal numbers in 3 ways.
24576633 = 74² + 329² + 4946² is the sum of 3 positive squares.
24576633² is the sum of 2 positive squares in 1 way.
24576633² is the sum of 3 positive squares.
24576633 is a divisor of 17⁹⁰ - 1.

Number of the day: 61877321194

Properties of the number 61877321194:

61877321194 = 2 × 13 × 1543 × 1542383 is composite and squarefree.
61877321194 has 4 distinct prime factors, 16 divisors, 103 antidivisors and 28540236528 totatives.
61877321194 has an emirpimes digit sum 49 in base 10.
61877321194 is the sum of 2 positive triangular numbers.
61877321194 is the difference of 2 positive pentagonal numbers in 8 ways.
61877321194 is the sum of 3 positive squares.
61877321194² is the sum of 2 positive squares in 1 way.
61877321194 is a divisor of 1283^31294119 - 1.

Number of the day: 34951

Properties of the number 34951:

34951 = 7 × 4993 is semiprime and squarefree.
34951 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 29952 totatives.
34951 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 34951 results in an emirpimes.
34951 = 17476² - 17475² = 2500² - 2493² is the difference of 2 nonnegative squares in 2 ways.
34951 is the sum of 2 positive triangular numbers.
34951 is the difference of 2 positive pentagonal numbers in 2 ways.
34951 is not the sum of 3 positive squares.
34951² is the sum of 2 positive squares in 1 way.
34951 is a divisor of 269⁴⁸ - 1.
34951 = '3' + '4951' is the concatenation of 2 prime numbers.
34951 = '34' + '951' is the concatenation of 2 semiprime numbers.
34951 is an emirpimes in (at least) the following bases: 2, 5, 7, 9, 10, 11, 17, 18, 19, 25, 29, 31, 32, 33, 35, 39, 45, 50, 53, 54, 56, 58, 65, 73, 74, 80, 82, 85, 87, and 95.
34951 is palindromic in (at least) the following bases: 49, and 57.
34951 in base 16 = 8887 and consists of only the digits '7' and '8'.
34951 in base 49 = ERE and consists of only the digits 'E' and 'R'.
34951 in base 57 = AhA and consists of only the digits 'A' and 'h'.

The number 34951 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A115918: Numbers n such that sigma(n)-phi(n) is a 4th power.
A131211: a(n)=(n^5-n-30)/30.
A168476: Numbers that are the product of two distinct primes and they are partial sum of products of two distinct primes.
A239007: Difference between the smallest 10^n-digit member of a sexy prime pair and 10^(10^n - 1).

Number of the day: 6908

Properties of the number 6908:

6908 = 2² × 11 × 157 is the 6019^th composite number and is not squarefree.
6908 has 3 distinct prime factors, 12 divisors, 15 antidivisors and 3120 totatives.
6908 has a prime digit sum 23 in base 10.
6908 = 1728² - 1726² = 168² - 146² is the difference of 2 nonnegative squares in 2 ways.
6908 is the difference of 2 positive pentagonal numbers in 2 ways.
6908 is not the sum of 3 positive squares.
6908² is the sum of 2 positive squares in 1 way.
6908 is a divisor of 1583⁶ - 1.
6908 in base 29 = 866 and consists of only the digits '6' and '8'.
6908 in base 33 = 6bb and consists of only the digits '6' and 'b'.
6908 in base 41 = 44K and consists of only the digits '4' and 'K'.

The number 6908 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A096813: Backwards row convergent of triangle A096811, in which A096811(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and (k-2).
A113650: Fibonacci(p-J(p,5)) mod p^2, where p is the n-th prime and J is the Jacobi symbol.
A185943: Riordan array ((1/(1-x))^m,x*A000108(x)), m=2.
A206464: Number of length-n Catalan-RGS (restricted growth strings) such that the RGS is a valid mixed radix number in falling factorial basis.
A217354: Numbers n such that 8^n + 3 is prime.
A224038: T(n,k)=Number of nXk 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing
A234991: T(n,k)=Number of (n+1)X(k+1) 0..5 arrays with every 2X2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant stress tilted 1X1 tilings)
A246479: T(n,k)=Number of length n+3 0..k arrays with no pair in any consecutive four terms totalling exactly k
A257827: Positive integers whose square is the sum of 96 consecutive squares.
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

Number of the day: 4420965

Properties of the number 4420965:

4420965 = 3 × 5 × 294731 is a sphenic number and squarefree.
4420965 has 3 distinct prime factors, 8 divisors, 11 antidivisors and 2357840 totatives.
4420965 has a sphenic digit sum 30 in base 10.
4420965 has an oblong digit sum 30 in base 10.
4420965 = 2210483² - 2210482² = 736829² - 736826² = 442099² - 442094² = 147373² - 147358² is the difference of 2 nonnegative squares in 4 ways.
4420965 is the difference of 2 positive pentagonal numbers in 2 ways.
4420965 is the sum of 3 positive squares.
4420965² is the sum of 2 positive squares in 1 way.
4420965 is a divisor of 241²⁹⁴⁷³ - 1.
4420965 = '44209' + '65' is the concatenation of 2 semiprime numbers.

Number of the day: 65655260678

Properties of the number 65655260678:

65655260678 = 2 × 7 × 113 × 41501429 is composite and squarefree.
65655260678 has 4 distinct prime factors, 16 divisors, 69 antidivisors and 27888959616 totatives.
65655260678 has an oblong digit sum 56 in base 10.
65655260678 is the sum of 2 positive triangular numbers.
65655260678 is the difference of 2 positive pentagonal numbers in 4 ways.
65655260678 is the sum of 3 positive squares.
65655260678² is the sum of 2 positive squares in 4 ways.
65655260678 is a divisor of 1213¹⁷⁶³¹⁶ - 1.
65655260678 = '6' + '5655260678' is the concatenation of 2 semiprime numbers.

Number of the day: 659325

Properties of the number 659325:

659325 = 3 × 5² × 59 × 149 is the 605812^th composite number and is not squarefree.
659325 has 4 distinct prime factors, 24 divisors, 27 antidivisors and 343360 totatives.
659325 has a sphenic digit sum 30 in base 10.
659325 has an oblong digit sum 30 in base 10.
659325 is the difference of 2 nonnegative squares in 12 ways.
659325 is the sum of 2 positive triangular numbers.
659325 is the difference of 2 positive pentagonal numbers in 4 ways.
659325 is the sum of 3 positive squares.
659325² is the sum of 2 positive squares in 7 ways.
659325 is a divisor of 1297²⁰ - 1.
659325 = '6593' + '25' is the concatenation of 2 semiprime numbers.

Number of the day: 355420

Properties of the number 355420:

355420 = 2² × 5 × 13 × 1367 is the 325011^th composite number and is not squarefree.
355420 has 4 distinct prime factors, 24 divisors, 9 antidivisors and 131136 totatives.
355420 has a prime digit sum 19 in base 10.
355420 = 88856² - 88854² = 17776² - 17766² = 6848² - 6822² = 1432² - 1302² is the difference of 2 nonnegative squares in 4 ways.
355420 is the sum of 2 positive triangular numbers.
355420 is the difference of 2 positive pentagonal numbers in 3 ways.
355420 is not the sum of 3 positive squares.
355420² is the sum of 2 positive squares in 4 ways.
355420 is a divisor of 521⁶⁸³ - 1.

Number of the day: 624

Properties of the number 624:

624 = 2⁴ × 3 × 13 is the 509^th composite number and is not squarefree.
624 has 3 distinct prime factors, 20 divisors, 5 antidivisors and 192 totatives.
624 has an oblong digit sum 12 in base 10.
Reversing the decimal digits of 624 results in a sphenic number.
624 = (7 × 8)/2 + … + (15 × 16)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
624 = 157² - 155² = 80² - 76² = 55² - 49² = 43² - 35² = 32² - 20² = 25² - 1² is the difference of 2 nonnegative squares in 6 ways.
624 is the difference of 2 positive pentagonal numbers in 1 way.
624 is not the sum of 3 positive squares.
624² = 240² + 576² is the sum of 2 positive squares in 1 way.
624 is a divisor of 79² - 1.
624 = '62' + '4' is the concatenation of 2 semiprime numbers.
624 is palindromic in (at least) the following bases: 5, 7, 25, 38, 47, 51, and 77.
624 in base 5 = 4444 and consists of only the digit '4'.
624 in base 7 = 1551 and consists of only the digits '1' and '5'.
624 in base 12 = 440 and consists of only the digits '0' and '4'.
624 in base 17 = 22c and consists of only the digits '2' and 'c'.

The number 624 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000118: Number of ways of writing n as a sum of 4 squares; also theta series of lattice Z^4.
A001692: Number of irreducible polynomials of degree n over GF(5); dimensions of free Lie algebras.
A005114: Untouchable numbers, also called nonaliquot numbers: impossible values for sum of aliquot parts of n (A001065).
A005563: a(n) = n*(n+2) (or, (n+1)^2 - 1).
A007602: Numbers that are divisible by the product of their digits.
A023896: Sum of positive integers in smallest positive reduced residue system modulo n. a(1) = 1 by convention.
A033996: 8 times triangular numbers: a(n) = 4n(n+1).
A046306: Numbers that are divisible by exactly 6 primes with multiplicity.
A051876: 24-gonal numbers: a(n) = n*(11*n-10).
A118277: Generalized 9-gonal numbers.

Number of the day: 8528

Properties of the number 8528:

8528 = 2⁴ × 13 × 41 is the 7464^th composite number and is not squarefree.
8528 has 3 distinct prime factors, 20 divisors, 15 antidivisors and 3840 totatives.
8528 has a prime digit sum 23 in base 10.
Reversing the decimal digits of 8528 results in a semiprime.
8528 = 2133² - 2131² = 1068² - 1064² = 537² - 529² = 177² - 151² = 108² - 56² = 93² - 11² is the difference of 2 nonnegative squares in 6 ways.
8528 is the difference of 2 positive pentagonal numbers in 2 ways.
8528 is the sum of 3 positive squares.
8528 = 28² + 88² = 8² + 92² is the sum of 2 positive squares in 2 ways.
8528² is the sum of 2 positive squares in 4 ways.
8528 is a divisor of 1559² - 1.
8528 is palindromic in (at least) base 58.
8528 in base 57 = 2ZZ and consists of only the digits '2' and 'Z'.
8528 in base 58 = 2V2 and consists of only the digits '2' and 'V'.

The number 8528 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A001935: Number of partitions with no even part repeated; partitions of n in which no parts are multiples of 4.
A053701: Vertically symmetric numbers.
A083365: Expansion of psi(x) / phi(x) in powers of x where phi(), psi() are Ramanujan theta functions.
A124499: Number of 1-2-3-4 trees with n edges and with thinning limbs. A 1-2-3-4 tree is an ordered tree with vertices of outdegree at most 4. A rooted tree with thinning limbs is such that if a node has k children, all its children have at most k children.
A127226: a(0)=2, a(1)=2, a(n)=2*a(n-1)+6*a(n-2).
A183563: Number of partitions of n containing a clique of size 6.
A191830: Expansion of x^2*(2-3*x)/(1-x-x^2)^2.
A240734: Floor(6^n/(2+sqrt(5))^n).
A257368: Numbers n such that the decimal expansions of both n and n^2 have 2 as smallest digit and 8 as largest digit.
A270300: Numbers which are representable as a sum of thirteen but no fewer consecutive nonnegative integers.

Number of the day: 777020

Properties of the number 777020:

777020 = 2² × 5 × 38851 is the 714776^th composite number and is not squarefree.
777020 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 310800 totatives.
777020 has a prime digit sum 23 in base 10.
777020 = (555 × 556)/2 + … + (559 × 560)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
777020 = 194256² - 194254² = 38856² - 38846² is the difference of 2 nonnegative squares in 2 ways.
777020 is the difference of 2 positive pentagonal numbers in 2 ways.
777020 is not the sum of 3 positive squares.
777020² is the sum of 2 positive squares in 1 way.
777020 is a divisor of 223¹⁴⁰ - 1.
777020 in base 42 = AKKK and consists of only the digits 'A' and 'K'.

Number of the day: 919713374

Properties of the number 919713374:

919713374 = 2 × 23 × 883 × 22643 is composite and squarefree.
919713374 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 439345368 totatives.
Reversing the decimal digits of 919713374 results in a prime.
919713374 is the difference of 2 positive pentagonal numbers in 4 ways.
919713374 is the sum of 3 positive squares.
919713374 is a divisor of 337⁷⁴⁷¹⁸⁶ - 1.
919713374 = '919713' + '374' is the concatenation of 2 sphenic numbers.

Number of the day: 739303548967

Properties of the number 739303548967:

739303548967 = 3697 × 199973911 is semiprime and squarefree.
739303548967 has 2 distinct prime factors, 4 divisors, 47 antidivisors and 739103571360 totatives.
Reversing the decimal digits of 739303548967 results in an emirpimes.
739303548967 = 369651774484² - 369651774483² = 99988804² - 99985107² is the difference of 2 nonnegative squares in 2 ways.
739303548967 is the difference of 2 positive pentagonal numbers in 2 ways.
739303548967 is not the sum of 3 positive squares.
739303548967² is the sum of 2 positive squares in 1 way.
739303548967 is a divisor of 17^219971301 - 1.
739303548967 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 10, 11, 18, 20, 23, 27, 31, 39, 50, 52, 53, 61, 65, 71, 72, 79, 81, 84, 88, 90, 91, 92, and 93.