A063918 a(1) = 1 and - applying the sieve of Eratosthenes - for n > 1: a(n) = if n is prime then 0 else the first prime p which marks n as composite.

1, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 7, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Sep 04 2001

Keywords

• nonn

Comments

k > 1: a(k*2) = 2, as all even numbers > 2 are marked by 2; for all primes p: a(p^k) = p and a(i) < p for i < p^2.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A055396, A020639.

Programs

PARI

{ for (n=1, 1000, if (n==1, p=1, if (isprime(n), p=0, p=1; until (n%p == 0, p=nextprime(p + 1)))); write("b063918.txt", n, " ", p) ) } \\ Harry J. Smith, Sep 02 2009