scholarly journals Sumsets avoiding squarefree integers

2010 ◽  
Vol 143 (1) ◽  
pp. 51-57
Author(s):  
Jan-Christoph Schlage-Puchta
Keyword(s):  
Squarefree Integers

Distribution of Nonlinear Congruential Pseudorandom Numbers Modulo Almost Squarefree Integers

2006 ◽  
Vol 148 (4) ◽  
pp. 297-307 ◽  
Author(s):  
Edwin D. El-Mahassni ◽  
Igor E. Shparlinski ◽  
Arne Winterhof
Keyword(s):  
Pseudorandom Numbers ◽  
Squarefree Integers

The Error Term for the Squarefree Integers

1966 ◽  
Vol 9 (3) ◽  
pp. 303-306 ◽  
Author(s):  
L. Moser ◽  
R.A. MacLeod
Keyword(s):  
Error Term ◽  
Squarefree Integers

Let Q(x) denote the number of squarefree integers ≤ x. Recently K. Rogers [ l ] has shown that Q(x) ≥ 53x / 88 for all x, with equality only at x = 176. Define R(x) to be Q(x) - 6/п2 X. (We observe that and ) Our objective will be to examine R(x). In particular, we show that for all x and observe that for x ≥ 8.

scholarly journals On the difference between consecutive squarefree integers

1988 ◽  
Vol 49 (5) ◽  
pp. 435-447 ◽  
Author(s):  
S. Graham ◽  
G. Kolesnik
Keyword(s):  
Squarefree Integers ◽  
The Difference

scholarly journals Tight t-Designs and Squarefree Integers

1989 ◽  
Vol 10 (2) ◽  
pp. 113-135 ◽  
Author(s):  
E. Bannai ◽  
S.G. Hoggar
Keyword(s):  
Squarefree Integers

The distribution of squarefree integers in small intervals

1954 ◽  
Vol 21 (4) ◽  
pp. 629-637 ◽  
Author(s):  
Richard Bellman ◽  
Harold N. Shapiro
Keyword(s):  
Squarefree Integers

scholarly journals Converegence of a series leading to an analogue of Ramanujan's assertion on squarefree integers

2018 ◽  
Vol 38 (2) ◽  
pp. 83-87 ◽  
Author(s):  
G. Sudhaamsh Mohan Reddy ◽  
S Srinivas Rau ◽  
B. Uma
Keyword(s):  
Prime Ideal ◽  
Prime Number ◽  
Prime Number Theorem ◽  
Prime Divisors ◽  
Squarefree Integer ◽  
Squarefree Integers

Let d be a squarefree integer. We prove that(i) Pnμ(n)nd(n′) converges to zero, where n′ is the product of prime divisors of nwith ( dn ) = +1. We use the Prime Number Theorem.(ii) Q( dp )=+1(1 −1ps ) is not analytic at s=1, nor is Q( dp )=−1(1 −1ps ) .(iii) The convergence (i) leads to a proof that asymptotically half the squarefree ideals have an even number of prime ideal factors (analogue of Ramanujan’s assertion).

scholarly journals PRODUCTS OF SHIFTED PRIMES SIMULTANEOUSLY TAKING PERFECT POWER VALUES

2012 ◽  
Vol 92 (2) ◽  
pp. 145-154 ◽  
Author(s):  
TRISTAN FREIBERG
Keyword(s):  
Lower Bound ◽  
Prime Factors ◽  
Squarefree Integers ◽  
Shifted Primes

AbstractLet r be an integer greater than 1, and let A be a finite, nonempty set of nonzero integers. We obtain a lower bound for the number of positive squarefree integers n, up to x, for which the products ∏ p∣n(p+a) (over primes p) are perfect rth powers for all the integers a in A. Also, in the cases where A={−1} and A={+1}, we will obtain a lower bound for the number of such n with exactly r distinct prime factors.

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