Number of the day: 3657

Daniel Bernoulli was born on this day 321 years ago.

Properties of the number 3657:

3657 is a cyclic number.
3657 = 3 × 23 × 53 is a sphenic number and squarefree.
3657 has 3 distinct prime factors, 8 divisors, 23 antidivisors and 2288 totatives.
3657 has a semiprime digit sum 21 in base 10.
3657 has a Fibonacci digit sum 21 in base 10.
3657 has a triangular digit sum 21 in base 10.
3657 has a triangular digit product 630 in base 10.
Reversing the decimal digits of 3657 results in a semiprime.
3657 = 1829² - 1828² = 611² - 608² = 91² - 68² = 61² - 8² is the difference of 2 nonnegative squares in 4 ways.
3657 is the sum of 2 positive triangular numbers.
3657 is the difference of 2 positive pentagonal numbers in 1 way.
3657 = 2² + 17² + 58² is the sum of 3 positive squares.
3657² = 1932² + 3105² is the sum of 2 positive squares in 1 way.
3657² is the sum of 3 positive squares.
3657 is a proper divisor of 1931⁴ - 1.
3657 is palindromic in (at least) the following bases: 68, -42, and -43.
3657 in base 8 = 7111 and consists of only the digits '1' and '7'.
3657 in base 42 = 233 and consists of only the digits '2' and '3'.

The number 3657 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A033816: a(n) = 2*n^2 + 3*n + 3.
A039665: Sets of 4 consecutive numbers with equal number of divisors.
A086381: Numbers n such that p=n^2+2 and p+2 are primes.
A111133: Number of partitions of n into at least two distinct parts.
A135703: a(n) = n*(7*n-2).
A151542: Generalized pentagonal numbers: a(n) = 12*n + 3*n*(n-1)/2.
A179791: Values x for records of minima of positive distance d between a ninth power of positive integer x and a square of integer y such d = x^9 - y^2 (x<>k^2 and y<>k^9).
A302069: T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
A306670: Numbers k with exactly three distinct prime factors and such that cototient(k) is a square.
A319060: A(n, k) is the k-th number b > 1 such that b^(prime(n+i)-1) == 1 (mod prime(n+i)^2) for each i = 0..2, with k running over the positive integers; square array, read by antidiagonals, downwards.