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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Tag Archives: Divisors
(a,b) such that d(a)=8, d(b)=18, ab=28
is the number of positive divisors of , including 1 and itself. is the sum of the positive divisors of , including 1 and itself is the sum … Continue reading
Puzzle – Sum of aliquot divisors of n
The aliquot divisors of n are the divisors of n less than n Find two squares such that if each is increased by the sum of its aliquot divisors the resulting … Continue reading
Integer n; n = k*d(n), d(n) is the number of divisors of n
is a positive integer and the number of divisors of Let’s find the lowest such that , Here’s a partial list k = 1 … 2 … Continue reading
Pairs (x,y); d(x) = d(y), σ(x) = σ(y), φ(x) = φ(y)
638 has 8 divisors: 1, 2, 11, 22, 29, 58, 319, 638 Sum of divisors: 1080 568 has 8 divisors: 1, 2, 4, 8, 71, 142, 284, 568 Sum of divisors: 1080 … Continue reading
SquareFree semiprimes n, σ(n), φ(n), and σ(n) * φ(n)
is the sum of divisors function Euler’s totient function is the number of positive integers not exceeding that have no common divisors with (other than the common divisor 1). In other words, … Continue reading
All positive divisors of N (except 1) contain the digit d = 1,2,…,9
Here are the smallest values for N I could find: 121 has 3 divisors : 1, 11, 121 All divisors of 121 contain the digit 1 254 … Continue reading
When (m,n) and (m+1,n+1) have the same prime divisors
Find pairs of different positive integers m and n such that >> have the same prime divisors >> have the same prime divisors For example, ; ………………. ……………… Other examples include: … Continue reading
Prime number 3
has 5 divisors: 1, 3, 9, 27, 81 Sum of divisors: Are there any other primes such that the sum of all positive integer divisors of … Continue reading
Num3er 2016 – sum of all the divisors
is the sum of all the divisors of Find other values for N for which Numbers of the form may satisfy the condition n … Continue reading
Distinct divisors of 12,24,36,… are sides of triangles
12 has 6 divisors: 1 2 3 4 6 12 24 has 8 divisors: 1 2 3 4 6 8 12 24 36 … Continue reading