J. Campbell

works on

conjecture disproof 1 divisor function 1 integer sequences 1 nondeficient numbers 1 perfect numbers 1

From the 1 of 8 linked papers with an AI index.

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20242026

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math.NT2026

Disproofs of two conjectures concerning nondeficient numbers

John M. Campbell

The paper disproves two recent conjectures that linked nondeficient integers with {‑1,1}-perfect numbers, showing the conjectured relationships do not hold.

math.NT2026

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

John M. Campbell, Shaun Cooper, Dongxi Ye

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

Disproofs of two conjectures concerning nondeficient numbers

Quadratic irrational analogues of Ramanujan's series for 1/I¨

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