A111565 Largest prime factor of prime power > 1 that divides the n-th composite number; or a(n) = 0 iff n-th composite number is equal to the product of distinct primes.

2, 0, 2, 3, 0, 2, 0, 0, 2, 3, 2, 0, 0, 2, 5, 0, 3, 2, 0, 2, 0, 0, 0, 3, 0, 0, 2, 0, 2, 3, 0, 2, 7, 5, 0, 2, 3, 0, 2, 0, 0, 2, 0, 3, 2, 0, 0, 2, 0, 0, 3, 0, 5, 2, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 3, 0, 2, 0, 0, 0, 2, 7, 3, 5, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 2, 3, 0, 0, 2, 11, 0, 0, 2, 5, 3, 2, 0, 0, 2, 0, 0, 3

Offset

1,1

Links

Table of n, a(n) for n=1..102.

Example

a(6) = 2 because C(6) = 12 = 3*2^2 and the largest prime factor of power 2^2 is 2.
a(28) = 0 because C(28) = 42 = 2*3*7 is the product of distinct primes

Prog

(PARI) A002808(n)={for(k=0, primepi(n), isprime(n++)&k--); n} A111565(n)={local(f, r, i); f=factor(A002808(n)); r=0; i=matsize(f)[1]; while((r==0)&&(i>0), if(f[i, 2]>1, r=f[i, 1], i--)); r}

Crossrefs

Cf. A002808 (composite numbers)

Sequence in context: A058623 A209689 A204329 * A299761 A141099 A127710

Adjacent sequences: A111562 A111563 A111564 * A111566 A111567 A111568

Keyword

nonn

Author

Giovanni Teofilatto, Nov 17 2005

Extensions

a(28) changed by Michael B. Porter, Feb 02 2010

Status

approved