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Natural number
← 743 744 745 → Cardinal seven hundred forty-four Ordinal 744th744 (seven hundred [and] forty four) is the natural number following 743 and preceding 745.
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 ( τ ) = q − 1 + 744 + 196 884 q + 21 493 760 q 2 + 864 299 970 q 3 + ⋯ , {\displaystyle j(\tau )=q^{-1}+744+196\,884q+21\,493\,760q^{2}+864\,299\,970q^{3}+\cdots ,} where q = e 2 π i τ {\displaystyle q=e^{2\pi i\tau }} . One consequence of this is that 744 appears in expressions for Ramanujan's constant and other almost integers.
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