Number of the day: 5195

Arthur Cayley was born on this day 199 years ago.

Properties of the number 5195:

5195 is a cyclic number.
5195 = 5 × 1039 is semiprime and squarefree.
5195 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 4152 totatives.
5195 has an oblong digit sum 20 in base 10.
5195 = 2598² - 2597² = 522² - 517² is the difference of 2 nonnegative squares in 2 ways.
5195 is the sum of 2 positive triangular numbers.
5195 is the difference of 2 positive pentagonal numbers in 2 ways.
5195 = 9² + 25² + 67² is the sum of 3 positive squares.
5195² = 3117² + 4156² is the sum of 2 positive squares in 1 way.
5195² is the sum of 3 positive squares.
5195 is a proper divisor of 271¹⁷³ - 1.
5195 = '51' + '95' is the concatenation of 2 semiprime numbers.
5195 is an emirpimes in (at least) the following bases: 8, 9, 11, 12, 13, 14, 15, 19, 22, 25, 28, 32, 35, 40, 51, 54, 55, 58, 60, 62, 63, 65, 68, 70, 75, 77, 81, 88, 89, 91, 93, and 99.
5195 is palindromic in (at least) the following bases: 30, 53, -44, and -98.
5195 in base 30 = 5n5 and consists of only the digits '5' and 'n'.
5195 in base 41 = 33T and consists of only the digits '3' and 'T'.
5195 in base 52 = 1ll and consists of only the digits '1' and 'l'.
5195 in base 53 = 1j1 and consists of only the digits '1' and 'j'.

The number 5195 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A067989: Row sums of triangle A067979; also of triangle A067990.
A088943: a(n)=60*sum(1<=i<=j<=k<=n,i*j^2/k).
A112068: Positive integers i for which A112049(i) == 8.
A124209: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + ... + n^61 + n^63 is prime.
A183564: Number of partitions of n containing a clique of size 7.
A238708: Number of strict partitions of n that include a pair of consecutive integers.
A241078: T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..2 introduced in row major order
A246211: Self-inverse permutation of natural numbers: a(0) = 0, a(1) = 1, and for n > 1, if A117966(n) < 0, a(n) = A117967(1+a(-(A117966(n)))), otherwise a(n) = A117968(a(A117966(n)-1)).
A279700: Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood.
A294587: Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of Product_{j>=1} (1 - j*x^j)^(j^k).