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744 (number)

FieldValue
number744
divisor1, 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. It is also an abundant number.

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: 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

References

  1. {{Cite OEIS. A005835. Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.
  2. {{Cite OEIS. A005101. Abundant numbers (sum of divisors of m exceeds 2m).
  3. {{Cite OEIS. A033880. Abundance of n, or (sum of divisors of n) - 2n.
  4. (1999). "Ramanujan and the modular j-invariant". [[Canadian Mathematical Bulletin]].
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integers moonshine-theory
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