744 (number) explained

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 -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] $$j(\backslash tau)\; =\; q^\; +\; 744\; +\; 196\backslash ,884\; q\; +\; 21\backslash ,493\backslash ,760\; q^2\; +\; 864\backslash ,299\backslash ,970\; q^3\; +\; \backslash cdots,$$where

q = e ^{2\pi} . One consequence of this is that 744 appears in expressions for Ramanujan's constant and other almost integers.

See also

• Moonshine theory

References

Notes and References

1. 2023-04-03 .
2. 2023-04-03 .
3. 2023-12-29 .
4. Berndt . Bruce C. . Bruce C. Berndt . Chan . Heng Huat . 1999 . Ramanujan and the modular j-invariant . . 42 . 4 . 427–440 . 10.4153/CMB-1999-050-1 . 1727340 . 1816362 . free.