Saturday, July 29, 2017

Number of the day: 4604

Properties of the number 4604:

4604 = 22 × 1151 is the 3980th composite number and is not squarefree.
4604 has 2 distinct prime factors, 6 divisors, 15 antidivisors and 2300 totatives.
4604 has a semiprime digit sum 14 in base 10.
4604 = 11522 - 11502 is the difference of 2 nonnegative squares in 1 way.
4604 is the difference of 2 positive pentagonal numbers in 1 way.
4604 is not the sum of 3 positive squares.
46042 is the sum of 3 positive squares.
4604 is a proper divisor of 68310 - 1.
4604 is palindromic in (at least) the following bases: 18, -43, and -59.
4604 in base 17 = ffe and consists of only the digits 'e' and 'f'.
4604 in base 18 = e3e and consists of only the digits '3' and 'e'.

The number 4604 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004112: Numbers n where |cos(n)| (or |cosec(n)| or |cot(n)|) decreases monotonically to 0; also |tan(n)|, |sec(n)|, |sin(n)| increases.
A046964: Sin(n) decreases monotonically to -1.
A054098: Triangular array generated by its row sums: T(n,0)=1 for n >= 0, T(1,1)=2, T(n,k)=T(n,k-1)+d*r(n-k) for k=2,3,...,n, d=(-1)^(k+1), n >= 2, r(h)=sum of the numbers in row h of T.
A065850: Let u be any string of n digits from {0,...,8}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u; then a(n) = max_u f(u).
A066857: Smallest number k such that n! - k is a square
A085329: Non-palindromic solutions to sigma(Rev(n)) = sigma(n).
A139479: Numbers n such that 24n+7 belongs to A000043.
A156167: Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).
A220681: T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical and antidiagonal neighbors, without consecutive collinear links
A237834: Number of partitions of n such that (greatest part) - (least part) >= number of parts.

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