## Hermann Minkowski was born on this day 153 years ago.

### Properties of the number 1509:

1509 is a cyclic number.1509 = 3 × 503 is semiprime and squarefree.

1509 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 1004 totatives.

1509 has an emirpimes digit sum 15 in base 10.

1509 has a triangular digit sum 15 in base 10.

1509 has sum of divisors equal to 2016 which is a triangular number.

Reversing the decimal digits of 1509 results in a sphenic number.

1509 = 755

^{2}- 754

^{2}= 253

^{2}- 250

^{2}is the difference of 2 nonnegative squares in 2 ways.

1509 is the sum of 2 positive triangular numbers.

1509 is the difference of 2 positive pentagonal numbers in 1 way.

1509 = 8

^{2}+ 17

^{2}+ 34

^{2}is the sum of 3 positive squares.

1509

^{2}is the sum of 3 positive squares.

1509 is a proper divisor of 7

^{251}- 1.

1509 is an emirpimes in (at least) the following bases: 4, 6, 9, 11, 12, 15, 18, 19, 20, 22, 24, 32, 36, 38, 41, 42, 47, 49, 55, 57, 59, 60, 64, 65, 71, 75, 77, 83, 84, 87, 91, 93, 96, 98, and 99.

1509 is palindromic in (at least) the following bases: 16, 29, -52, and -58.

1509 in base 16 = 5e5 and consists of only the digits '5' and 'e'.

1509 in base 28 = 1pp and consists of only the digits '1' and 'p'.

1509 in base 29 = 1n1 and consists of only the digits '1' and 'n'.

1509 in base 38 = 11R and consists of only the digits '1' and 'R'.

### The number 1509 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A005228: Sequence and first differences (A030124) together list all positive numbers exactly once.

A006832: Discriminants of totally real cubic fields.

A026105: Triangle T read by rows: differences of Motzkin triangle (A026300).

A059993: Pinwheel numbers: a(n) = 2*n^2 + 6*n + 1.

A094612: Fundamental discriminants of real quadratic number fields with class number 3.

A165652: Number of disconnected 2-regular graphs on n vertices.

A202124: T(n,k)=Number of -k..k arrays of n elements with first, second and third differences also in -k..k

A224146: T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing

A241306: T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4

A279567: Number of length n inversion sequences avoiding the patterns 100, 110, 120, and 210.

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