| Number | 744 |
|---|---|
| Divisor | 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744 |
744 (seven hundred [and] forty four) is the natural number following 743 and preceding 745.
In mathematics
744 is a semiperfect number.[1] It is also an abundant number.[2][3]
The j-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:[4]
j(\tau) = q^{-1} + 744 + 196\,884 q + 21\,493\,760 q^2 + 864\,299\,970 q^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.
References
- ^ Retrieved 2023-04-03.
- ^ Retrieved 2023-04-03.
- ^ Retrieved 2023-12-29.
- ^ Berndt, Bruce C. & Chan, Heng Huat (1999). "Ramanujan and the modular j-invariant". Canadian Mathematical Bulletin. 42 (4): 427–440. doi:10.4153/CMB-1999-050-1. MR 1727340. S2CID 1816362