OFFSET
0,3
COMMENTS
For n >= 2 this is the cototient(A051953) + 1. If n = p*q for different primes p and q, a(n) = p + q. - Wesley Ivan Hurt, Aug 27 2013
If n is the product of twin primes, (a(n) +- 2)/2 gives the two primes. - Wesley Ivan Hurt, Sep 06 2013
LINKS
Peter Luschny, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = n - phi(n) + 1 for n >= 2. (previous name)
From Wesley Ivan Hurt, Aug 27 2013: (Start)
a(n) = A051953(n) + 1 for n >= 2.
a(n) = n - A000010(n) + 1 for n >= 2.
a(n) = 2*A067392(n)/n for n > 1. - Robert G. Wilson v, Jul 16 2019
EXAMPLE
a(10) = 7, since 10 - phi(10) + 1 = 10 - 4 + 1 = 7. Also, since 10 is a squarefree semiprime, 7 represents the sum of the distinct prime factors of 10.
MAPLE
with(numtheory); 1, 0, seq(k - phi(k) + 1, k = 2..70);
# Wesley Ivan Hurt, Aug 27 2013
K := (n, k) -> NumberTheory:-KroneckerSymbol(n, k):
seq(nops(select(k -> K(n, k) = 0, [seq(0..n)])), n = 0..70);
# Alternative:
T := (n, k) -> ifelse(NumberTheory:-AreCoprime(n, k), 1, 0):
seq(nops(select(k -> T(n, k) = 0, [seq(0..n)])), n = 0..70);
# Peter Luschny, May 15 2024
MATHEMATICA
Table[n - EulerPhi[n] + 1 - Boole[n == 1], {n, 0, 70}]
(* Wesley Ivan Hurt, Aug 27 2013 *)
Table[Count[Table[KroneckerSymbol[n, k], {k, 0, n}], 0], {n, 0, 70}]
(* Peter Luschny, May 15 2024 *)
PROG
(PARI) j=[1, 0]; for(n=2, 200, j=concat(j, n+1-eulerphi(n))); j
(SageMath)
print([sum(kronecker(n, k) == 0 for k in range(n + 1)) for n in range(70)])
# Peter Luschny, May 16 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 20 2001
EXTENSIONS
Offset set to 0, a(0) = 1 added, a(1) adapted and new name by Peter Luschny, May 15 2024
STATUS
approved