Thursday, February 9, 2017

Number of the day: 9641

Properties of the number 9641:

9641 = 31 × 311 is semiprime and squarefree.
9641 has 2 distinct prime factors, 4 divisors, 7 antidivisors and 9300 totatives.
9641 has an oblong digit sum 20 in base 10.
Reversing the decimal digits of 9641 results in an emirpimes.
9641 = 48212 - 48202 = 1712 - 1402 is the difference of 2 nonnegative squares in 2 ways.
9641 is the sum of 2 positive triangular numbers.
9641 is the difference of 2 positive pentagonal numbers in 2 ways.
9641 = 12 + 62 + 982 is the sum of 3 positive squares.
96412 is the sum of 3 positive squares.
9641 is a divisor of 154910 - 1.
9641 is an emirpimes in (at least) the following bases: 2, 5, 6, 8, 10, 11, 13, 15, 16, 20, 21, 23, 25, 27, 33, 34, 36, 40, 45, 49, 50, 51, 53, 54, 56, 61, 64, 66, 70, 72, 73, 74, 75, 76, 78, 79, 81, 82, 84, 85, 86, 88, 91, 94, 98, and 99.
9641 is palindromic in (at least) the following bases: 32, 63, -5, -24, -25, -30, -41, -44, -61, and -81.
9641 in base 4 = 2112221 and consists of only the digits '1' and '2'.
9641 in base 24 = ghh and consists of only the digits 'g' and 'h'.
9641 in base 29 = bdd and consists of only the digits 'b' and 'd'.
9641 in base 32 = 9d9 and consists of only the digits '9' and 'd'.
9641 in base 40 = 611 and consists of only the digits '1' and '6'.
9641 in base 43 = 599 and consists of only the digits '5' and '9'.
9641 in base 62 = 2VV and consists of only the digits '2' and 'V'.

The number 9641 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A007419: Largest number not the sum of distinct n-th-order polygonal numbers.
A020223: Pseudoprimes to base 95.
A048698: Nonprime numbers n such that sum of aliquot divisors of n is a cube.
A049048: Composite numbers n such that k! == 1 (mod n) for some k > 2.
A055437: a(n) = 10*n^2+n.
A128356: Least number k>1 (that is not the power of prime p) such that k divides (p+1)^k-1, where p = prime(n).
A128452: Least number k>n such that k^2 divides n^k - 1.
A134602: Composite numbers such that the square mean of their prime factors is a nonprime integer (where the prime factors are taken with multiplicity and the square mean of c and d is sqrt((c^2+d^2)/2)).
A135789: Positive numbers of the form x^4 - 6 * x^2 * y^2 + y^4 (where x,y are integers).
A247137: Numbers for which the root mean square of nontrivial divisors is an integer and which are not a square of prime numbers.

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