Numbers Personalities Patterns

Symbols used in this Book
A.P
Arithmetic Progression
G.P
Geometric Progression
H.P
Harmonic Progression
(a, b) = 1
a is relatively prime to b or g.c.d of a and b is 1
(a, b) c
g.c.d of a and b is c
alb
a divides b
Bn
ath Bernoulli number
ab(mod c)
ab is divisible by c
d (n)
Number of positive divisors of n
Hn
nth hex number
wth hexagonal number
Pn
nth pentagonal number
Pn
ath Pell number
Hepn
with heptagonal number
Nn
ath nonagonal number
Ocin
nth octagonal number
Tein
wth tetrahedral number
Sqpn
ith square pyramidal number
nth triangular number
Tn
nth Fibonacci number
Fn
Fermat number 22" + 1
fn
nth Lucas number
Ln
Mersenne number 2" - 1
ath pyramidal number
(n)
sum of the digits of n
spen)
sum of the digits of prime factors
(n)
sum of the divisors of n
σ(π)
sum of the unitary divisors of n
sum of the bi-unitary divisors of n
p(n)
number of partitions of n
M(p)
multiple of p
Kn
number formed with digit k repeated n times
R
number formed with n repeated units
P(n)
product of all divisors of n
(n)
GSK
number of positive integers not exceeding
that are relatively prime to n
Pseudo Fibonacci Number
Legendre symbol
number of combinations of n things taken at a time and is equal to n!/(nr)! r!
n!
1-2-3-... (n-1) (л)
In
111 1! 2! 3! 1--+- ++(-1) n!
2.4.6. n, if n is even 1-3-5 n, if n is odd difference between m and n
pi. 3. 14159...
...