## Sophie Germain was born on this day 241 years ago.

## Alexander Craig Aitken was born on this day 122 years ago.

### Properties of the number 7824:

7824 = 2^{4}× 3 × 163 is the 6834

^{th}composite number and is not squarefree.

7824 has 3 distinct prime factors, 20 divisors, 3 antidivisors and 2592 totatives.

7824 has a semiprime digit sum 21 in base 10.

7824 has a Fibonacci digit sum 21 in base 10.

7824 has a triangular digit sum 21 in base 10.

Reversing the decimal digits of 7824 results in a semiprime.

7824 = 1957

^{2}- 1955

^{2}= 980

^{2}- 976

^{2}= 655

^{2}- 649

^{2}= 493

^{2}- 485

^{2}= 332

^{2}- 320

^{2}= 175

^{2}- 151

^{2}is the difference of 2 nonnegative squares in 6 ways.

7824 is the difference of 2 positive pentagonal numbers in 1 way.

7824 = 4

^{2}+ 8

^{2}+ 88

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

7824

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

7824 is a divisor of 977

^{2}- 1.

7824 is palindromic in (at least) base -46.

7824 in base 5 = 222244 and consists of only the digits '2' and '4'.

7824 in base 25 = cco and consists of only the digits 'c' and 'o'.

7824 in base 39 = 55O and consists of only the digits '5' and 'O'.

7824 in base 62 = 22C and consists of only the digits '2' and 'C'.

### The number 7824 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A067153: Number of regions in regular n-gon which are hexagons.

A073118: Total sum of prime parts in all partitions of n.

A087316: a(n) = Sum_{k=1..n} prime(k)^prime(n-k+1).

A128129: Expansion of (chi(-q^3)/ chi^3(-q) -1)/3 in powers of q where chi() is a Ramanujan theta function.

A132975: Expansion of q * psi(-q^9) / psi(-q) in powers of q where psi() is a Ramanujan theta function.

A132977: Expansion of q^(-1/3) * (eta(q^6)^4 / (eta(q) * eta(q^3) * eta(q^4) * eta(q^12)))^2 in powers of q.

A152760: 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).

A182977: Total number of parts that are neither the smallest part nor the largest part in all partitions of n.

A194560: G.f.: Sum_{n>=1} G_n(x)^n where G_n(x) = x + x*G_n(x)^n.

A204432: Permanent of the n-th principal submatrix of A204431.

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