| ||||
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Cardinal | seven hundred forty-four | |||
Ordinal | 744th (seven hundred forty-fourth) | |||
Factorization | 23 × 3 × 31 | |||
Divisors | 1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 124, 186, 248, 372, 744 | |||
Greek numeral | ΨΜΔ´ | |||
Roman numeral | DCCXLIV | |||
Binary | 10111010002 | |||
Ternary | 10001203 | |||
Senary | 32406 | |||
Octal | 13508 | |||
Duodecimal | 52012 | |||
Hexadecimal | 2E816 |
744 (seven hundred [and] forty four) is the natural number following 743 and preceding 745.
744 plays a major role within moonshine theory of sporadic groups.
In Mathematics
744 is a semiperfect number.[1] It is also an abundant number.[2][3]
The j–invariant can be written as a q–expansion Fourier series.[4] where . a complex variable that represents the half-period ratio.
See also
References
- ^ Sloane, N. J. A. (ed.). "Sequence A005835 (Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-03.
- ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-04-03.
- ^ Sloane, N. J. A. (ed.). "Sequence A033880 (Abundance of n, or (sum of divisors of n) - 2n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 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.