Tuesday, August 22, 2017

Number of the day: 3974

Properties of the number 3974:

3974 = 2 × 1987 is semiprime and squarefree.
3974 has 2 distinct prime factors, 4 divisors, 5 antidivisors and 1986 totatives.
3974 has a prime digit sum 23 in base 10.
3974 has an oblong digit product 756 in base 10.
Reversing the decimal digits of 3974 results in a prime.
3974 = 302 + … + 332 is the sum of at least 2 consecutive positive squares in 1 way.
3974 = 12 + 22 + 632 is the sum of 3 positive squares.
39742 is the sum of 3 positive squares.
3974 is a proper divisor of 6473 - 1.
3974 = '39' + '74' is the concatenation of 2 semiprime numbers.
3974 is an emirpimes in (at least) the following bases: 5, 6, 8, 12, 13, 16, 19, 20, 25, 26, 28, 29, 35, 36, 38, 39, 42, 44, 47, 48, 54, 56, 57, 59, 60, 63, 64, 67, 68, 71, 74, 75, 80, 81, 84, 86, 91, and 100.
3974 is palindromic in (at least) the following bases: 17, and 27.
3974 in base 17 = dcd and consists of only the digits 'c' and 'd'.
3974 in base 26 = 5mm and consists of only the digits '5' and 'm'.
3974 in base 27 = 5c5 and consists of only the digits '5' and 'c'.
3974 in base 31 = 446 and consists of only the digits '4' and '6'.
3974 in base 44 = 22E and consists of only the digits '2' and 'E'.

The number 3974 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007684: Prime(n)*...*prime(a(n)) is the least product of consecutive primes that is non-deficient.
A007707: Prime(n)*...*prime(a(n)) is the least product of consecutive primes which is abundant.
A027575: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2.
A059886: a(n) = |{m : multiplicative order of 4 mod m=n}|.
A068336: a(1) = 1; a(n+1) = 1 + sum{k|n} a(k), sum is over the positive divisors, k, of n.
A081268: Diagonal of triangular spiral in A051682.
A104577: Indices of prime generalized tetranacci numbers, A073817.
A191455: Dispersion of (floor(n*e)), by antidiagonals.
A218064: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 nXk array
A227743: Integers n for which A173318(n) is a square.

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