Tag Archives: Divisors

(a,b) such that d(a)=8, d(b)=18, |a-b|=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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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