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The blue line picks only the values of n that are multiples of 121. The Ramanujan tau function , studied by Ramanujan ( 1916 ), is the function τ : N → Z {\displaystyle \tau :\mathbb {N} \rightarrow \mathbb {Z} } defined by the following identity:
Sieve of Eratosthenes: algorithm steps for primes below 121 (including optimization of starting from prime's square). In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit.
Cycles of the unit digit of multiples of integers ending in 1, 3, 7 and 9 (upper row), and 2, 4, 6 and 8 (lower row) on a telephone keypad. Figure 1 is used for multiples of 1, 3, 7, and 9. Figure 2 is used for the multiples of 2, 4, 6, and 8. These patterns can be used to memorize the multiples of any number from 0 to 10, except 5.
Multiples of this unit then became the second numbers, ... 121 61 10 366: Unviginticentillion Unsexagintillion Unsexagintillion 130 65 10 393: Trigintacentillion
When a prime occurs multiple times, exponentiation can be used to group together multiple copies of the same prime number: for example, ... [121] In particular ...
In mathematics, a multiple is the product of any quantity and an integer. [1] In other words, for the quantities a and b , it can be said that b is a multiple of a if b = na for some integer n , which is called the multiplier .
1188 = first 4 digit multiple of 18 to contain 18 [163] 1189 = number of squares between 35 2 and 35 4. [114] 1190 = pronic number, [51] number of cards to build a 28-tier house of cards [164] 1191 = 35 2 - 35 + 1 = H 35 (the 35th Hogben number) [165] 1192 = sum of totient function for first 62 integers; 1193 = a number such that 4 1193 - 3 ...
The exponent of the group, that is, the least common multiple of the orders in the cyclic groups, is given by the Carmichael function (sequence A002322 in the OEIS). In other words, λ ( n ) {\displaystyle \lambda (n)} is the smallest number such that for each a coprime to n , a λ ( n ) ≡ 1 ( mod n ) {\displaystyle a^{\lambda (n)}\equiv 1 ...