J. Campbell

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20232026

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math.NT2026

Disproofs of two conjectures concerning nondeficient numbers

John M. Campbell

A positive integer $n$ is said to be nondeficient if $σ (n) \geq 2 n$ . Letting the positive divisors of a positive integer $n$ be written as $1 = d_0 < d_1 < \cdots < d_k < d_{k+1} =…

math.NT2026

Quadratic irrational analogues of Ramanujan's series for $1/ π$

John M. Campbell, Shaun Cooper, Dongxi Ye

About 40 years ago Jonathan and Peter Borwein discovered the series identity $n = 0 \sum \infty \frac{( - 1 ) ^{n} ( 6 n )!}{( 3 n )! ( n ! ) ^{3}} \frac{( A + n B )}{C ^{n + 1/2}} = \frac{1}{12 π}$ where…

Disproofs of two conjectures concerning nondeficient numbers

Quadratic irrational analogues of Ramanujan's series for 1/π

Quadratic irrational analogues of Ramanujan's series for $1/ π$