225 (number)
In the following article, we will explore the fascinating world of 225 (number). From its impact on society to its multiple applications in different areas, 225 (number) has captured the attention of people of all ages and interests. We will delve into its history, analyze its relevance today, and discuss possible future prospects. Additionally, we will closely examine the benefits and challenges that 225 (number) presents, offering a complete and balanced view of this exciting topic. Join us on this journey to discover everything 225 (number) has to offer.
225 (two hundred twenty-five) is the natural number following 224 and preceding 226.
In mathematics
| ||||
|---|---|---|---|---|
| Cardinal | two hundred twenty-five | |||
| Ordinal | 225th (two hundred twenty-fifth) | |||
| Factorization | 32 × 52 | |||
| Prime | no | |||
| Greek numeral | ΣΚΕ´ | |||
| Roman numeral | CCXXV, ccxxv | |||
| Binary | 111000012 | |||
| Ternary | 221003 | |||
| Senary | 10136 | |||
| Octal | 3418 | |||
| Duodecimal | 16912 | |||
| Hexadecimal | E116 | |||
225 is the smallest number that is a polygonal number in five different ways.[1] It is a square number (225 = 152),[2] an octagonal number,[3] and a squared triangular number (225 = (1 + 2 + 3 + 4 + 5)2 = 13 + 23 + 33 + 43 + 53) .[4]
As the square of a double factorial, 225 = 5!!2 counts the number of permutations of six items in which all cycles have even length, or the number of permutations in which all cycles have odd length.[5] And as one of the Stirling numbers of the first kind, it counts the number of permutations of six items with exactly three cycles.[6]
225 is a highly composite odd number, meaning that it has more divisors than any smaller odd numbers.[7] After 1 and 9, 225 is the third smallest number n for which σ(φ(n)) = φ(σ(n)), where σ is the sum of divisors function and φ is Euler's totient function.[8] 225 is a refactorable number.[9]
225 is the smallest square number to have one of every digit in some number base (225 is 3201 in base 4) [10]
225 is the smallest odd number with exactly nine divisors.[11]
References
- ^ Sloane, N. J. A. (ed.). "Sequence A063778 (a(n) = the least integer that is polygonal in exactly n ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000290 (The squares)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000537 (Sum of first n cubes; or n-th triangular number squared)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001818 (Squares of double factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000399 (Unsigned Stirling numbers of first kind s(n,3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053624 (Highly composite odd numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033632 (Numbers n such that sigma(phi(n)) = phi(sigma(n)))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-04-18. Retrieved 2016-04-18.
- ^ Sloane, N. J. A. (ed.). "Sequence A061845 (Numbers which have one of every digit in some base)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000005 (the number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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