Sunday, August 28, 2016

Number of the day: 4018282980

Properties of the number 4018282980:

4018282980 = 22 × 3 × 5 × 53 × 101 × 12511 is the 3827495000th composite number and is not squarefree.
4018282980 has 6 distinct prime factors, 96 divisors, 37 antidivisors and 1040832000 totatives.
4018282980 has a sphenic digit sum 42 in base 10.
4018282980 has an oblong digit sum 42 in base 10.
4018282980 is the difference of 2 nonnegative squares in 16 ways.
4018282980 is the difference of 2 positive pentagonal numbers in 6 ways.
4018282980 = 3702 + 26842 + 633322 is the sum of 3 positive squares.
40182829802 = 27564235202 + 29238207002 = 4508463962 + 39929106722 = 6852024482 + 39594312362 = 17266681322 + 36283901762 = 7956996002 + 39387130202 = 26735506562 + 29997874922 = 14052355202 + 37645599002 = 11345475242 + 38547892322 = 21685066082 + 33829243562 = 21228664802 + 34117497002 = 3487566362 + 40031196482 = 14556798722 + 37453430042 = 24109697882 + 32146263842 is the sum of 2 positive squares in 13 ways.
40182829802 is the sum of 3 positive squares.
4018282980 is a divisor of 12291170 - 1.

Saturday, August 27, 2016

Number of the day: 81326848

Giuseppe Peano was born on this day 158 years ago.

Properties of the number 81326848:

81326848 = 28 × 107 × 2969 is the 76584398th composite number and is not squarefree.
81326848 has 3 distinct prime factors, 36 divisors, 23 antidivisors and 40269824 totatives.
81326848 is the difference of 2 nonnegative squares in 14 ways.
81326848 is the sum of 2 positive triangular numbers.
81326848 is the difference of 2 positive pentagonal numbers in 1 way.
81326848 = 3042 + 8162 + 89762 is the sum of 3 positive squares.
813268482 = 63275522 + 810803202 is the sum of 2 positive squares in 1 way.
813268482 is the sum of 3 positive squares.
81326848 is a divisor of 1663212 - 1.

Friday, August 26, 2016

Number of the day: 6545

Properties of the number 6545:

6545 = 5 × 7 × 11 × 17 is the 5700th composite number and is squarefree.
6545 has 4 distinct prime factors, 16 divisors, 23 antidivisors and 3840 totatives.
6545 has an oblong digit sum 20 in base 10.
6545 has an oblong digit product 600 in base 10.
6545 = 112 + … + 272 is the sum of at least 2 consecutive positive squares in 1 way.
6545 = (1 × 2)/2 + … + (33 × 34)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6545 = 32732 - 32722 = 6572 - 6522 = 4712 - 4642 = 3032 - 2922 = 2012 - 1842 = 1112 - 762 = 872 - 322 = 812 - 42 is the difference of 2 nonnegative squares in 8 ways.
6545 is the sum of 2 positive triangular numbers.
6545 is the difference of 2 positive pentagonal numbers in 6 ways.
6545 = 102 + 192 + 782 is the sum of 3 positive squares.
65452 = 30802 + 57752 = 10012 + 64682 = 27722 + 59292 = 39272 + 52362 is the sum of 2 positive squares in 4 ways.
65452 is the sum of 3 positive squares.
6545 is a divisor of 14292 - 1.
6545 = '6' + '545' is the concatenation of 2 semiprime numbers.
6545 is palindromic in (at least) the following bases: 16, 21, 84, and -23.
6545 in base 16 = 1991 and consists of only the digits '1' and '9'.
6545 in base 21 = ehe and consists of only the digits 'e' and 'h'.
6545 in base 22 = dbb and consists of only the digits 'b' and 'd'.

The number 6545 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000292: Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.
A000447: a(n) = 1^2 + 3^2 + 5^2 + 7^2 + ... + (2*n-1)^2 = n*(4*n^2 - 1)/3.
A013594: Smallest order of cyclotomic polynomial containing n or -n as a coefficient.
A092269: Spt function: total number of smallest parts in all partitions of n.
A134605: Composite numbers such that the square root of the sum of squares of their prime factors (with multiplicity) is an integer.
A135602: Right-angled numbers with an internal digit as the vertex.
A138135: Number of parts > 1 in the last section of the set of partitions of n.
A152977: Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the number of partitions of 2^n into powers of 2 less than or equal to 2^k.
A248068: T(n,k)=Number of length n+5 0..k arrays with some disjoint triples in each consecutive six terms having the same sum
A255872: Smallest Rhonda number to base b = n-th composite number, cf. A002808.

Thursday, August 25, 2016

Number of the day: 34384

Properties of the number 34384:

34384 = 24 × 7 × 307 is the 30708th composite number and is not squarefree.
34384 has 3 distinct prime factors, 20 divisors, 13 antidivisors and 14688 totatives.
34384 has a semiprime digit sum 22 in base 10.
Reversing the decimal digits of 34384 results in a semiprime.
34384 = 85972 - 85952 = 43002 - 42962 = 21532 - 21452 = 12352 - 12212 = 6282 - 6002 = 3352 - 2792 is the difference of 2 nonnegative squares in 6 ways.
34384 is the sum of 2 positive triangular numbers.
34384 is the difference of 2 positive pentagonal numbers in 2 ways.
34384 = 722 + 922 + 1442 is the sum of 3 positive squares.
343842 is the sum of 3 positive squares.
34384 is a divisor of 176 - 1.
34384 is palindromic in (at least) the following bases: 33, 52, and 90.
34384 in base 33 = viv and consists of only the digits 'i' and 'v'.
34384 in base 52 = CbC and consists of only the digits 'C' and 'b'.
34384 in base 53 = CCe and consists of only the digits 'C' and 'e'.

The number 34384 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A057546: Number of Catalan objects of size n fixed by Catalan Automorphism A057511/A057512 (deep rotation of general parenthesizations/plane trees).
A059376: Jordan function J_3(n).
A063453: Multiplicative with a(p^e) = 1 - p^3.
A082261: Row sums in A082259.
A192349: Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
A211689: Number of -4..4 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two or three distinct values for every i<=n and j<=n

Wednesday, August 24, 2016

Number of the day: 3548

Properties of the number 3548:

3548 = 22 × 887 is the 3050th composite number and is not squarefree.
3548 has 2 distinct prime factors, 6 divisors, 17 antidivisors and 1772 totatives.
3548 has an oblong digit sum 20 in base 10.
3548 has sum of divisors equal to 6216 which is a triangular number.
Reversing the decimal digits of 3548 results in a semiprime.
3548 = 8882 - 8862 is the difference of 2 nonnegative squares in 1 way.
3548 is the difference of 2 positive pentagonal numbers in 1 way.
3548 is not the sum of 3 positive squares.
35482 is the sum of 3 positive squares.
3548 is a divisor of 13443 - 1.
3548 is palindromic in (at least) the following bases: 17, 20, and 23.
3548 in base 16 = ddc and consists of only the digits 'c' and 'd'.
3548 in base 17 = c4c and consists of only the digits '4' and 'c'.
3548 in base 20 = 8h8 and consists of only the digits '8' and 'h'.
3548 in base 22 = 776 and consists of only the digits '6' and '7'.
3548 in base 23 = 6g6 and consists of only the digits '6' and 'g'.
3548 in base 59 = 118 and consists of only the digits '1' and '8'.

The number 3548 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.
A008509: Numbers n such that n-th triangular number is palindromic.
A053618: a(n) = ceiling(C(n,4)/n).
A066321: Binary representation of base i-1 expansion of n: replace i-1 by 2 in base i-1 expansion of n.
A127764: Integer part of Gauss' Arithmetic-Geometric Mean M(2,n^3).
A234500: Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
A245173: Triangle read by rows: coefficients of the polynomials A_{3,4}(n,k).
A252993: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly 2 distinct values, in every diagonal 1 or 2 distinct values, in every antidiagonal 2 or 3 distinct values, and new values 0 upwards introduced in row major order
A261761: T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row and column prime, read as a binary number with top and left being the most significant bits.
A270980: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 237", based on the 5-celled von Neumann neighborhood.

Tuesday, August 23, 2016

Number of the day: 6165

Properties of the number 6165:

6165 = 32 × 5 × 137 is the 5361th composite number and is not squarefree.
6165 has 3 distinct prime factors, 12 divisors, 17 antidivisors and 3264 totatives.
6165 = (30 × 31)/2 + … + (39 × 40)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6165 = 30832 - 30822 = 10292 - 10262 = 6192 - 6142 = 3472 - 3382 = 2132 - 1982 = 912 - 462 is the difference of 2 nonnegative squares in 6 ways.
6165 is the difference of 2 positive pentagonal numbers in 1 way.
6165 = 542 + 572 = 92 + 782 is the sum of 2 positive squares in 2 ways.
6165 = 102 + 172 + 762 is the sum of 3 positive squares.
61652 = 39602 + 47252 = 3332 + 61562 = 14042 + 60032 = 36992 + 49322 is the sum of 2 positive squares in 4 ways.
61652 is the sum of 3 positive squares.
6165 is a divisor of 374 - 1.
6165 is palindromic in (at least) the following bases: 35, 67, -27, and -92.
6165 in base 26 = 933 and consists of only the digits '3' and '9'.
6165 in base 34 = 5bb and consists of only the digits '5' and 'b'.
6165 in base 35 = 515 and consists of only the digits '1' and '5'.
6165 in base 55 = 225 and consists of only the digits '2' and '5'.

The number 6165 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A045944: Rhombic matchstick numbers: n*(3*n+2).
A061541: Number of connected labeled graphs with n nodes and n+2 edges.
A062734: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, 0 <= k <= n(n-1)/2).
A073399: Coefficient triangle of polynomials (falling powers) related to convolutions of A001045(n+1), n>=0, (generalized (1,2)-Fibonacci). Companion triangle is A073400.
A123527: Triangular array T(n,k) giving number of connected graphs with n labeled nodes and k edges (n >= 1, n-1 <= k <= n(n-1)/2).
A164000: Main diagonal of array in A163280.
A166512: 2-comma numbers: n occurs in the sequence S[k+1]=S[k]+10*last_digit(S[k-1])+first_digit(S[k]) for two different splittings n=concat(S[0],S[1]).
A214359: Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
A228024: Antiharmonic mean of the divisors of A228023(n) (the n-th primitive antiharmonic number).
A262521: Numbers where A262520 takes a negative value; numbers n for which A155043(2n) > A155043(2n + 1).

Monday, August 22, 2016

Number of the day: 828606

Properties of the number 828606:

828606 = 2 × 3 × 138101 is a sphenic number and squarefree.
828606 has 3 distinct prime factors, 8 divisors, 9 antidivisors and 276200 totatives.
828606 has a sphenic digit sum 30 in base 10.
828606 has an oblong digit sum 30 in base 10.
828606 is the sum of 2 positive triangular numbers.
828606 is the difference of 2 positive pentagonal numbers in 2 ways.
828606 = 52 + 1662 + 8952 is the sum of 3 positive squares.
8286062 = 2156942 + 8000402 is the sum of 2 positive squares in 1 way.
8286062 is the sum of 3 positive squares.
828606 is a divisor of 7511381 - 1.