744 (number)

744 (seven hundred [and] forty four) is the natural number following 743 and preceding 745.

In mathematics

744 is a semiperfect number. It is also an abundant number.

The [[j-invariant|Template:Mvar-invariant]], an important function in the study of modular forms and Monstrous moonshine, can be written as a Fourier series in which the constant term is 744: $$j(\tau )=q^{-1}+744+196884q+21493760q^2+864299970q^3+\cdots ,$$where $q=e^{2\pi i\tau }$. One consequence of this is that 744 appears in expressions for Ramanujan's constant and other almost integers.

See also

• Moonshine theory

References

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