OFFSET
1,6
COMMENTS
For p prime, a(p^k) = ceiling(p^(k-1)/k); in particular, a(p) = 1. For p and q distinct primes, a(pq) = min(p,q).
a(n) >= n/sopfr(n), where sopfr is A001414; when the right hand side is an integer, this is an equality.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..12024
EXAMPLE
For n = 12, we have the representation 2+2+2+3+3. Since there are two 2's available, this can be done with 2 copies of the prime factors: 2+2'+3 from the first copy, and 2+3 from the second. Thus a(12) = 2.
PROG
(PARI) a(n)=local(fm, p); if(n<=1, return(0)); fm=factor(n); p=prod(i=1, matsize(fm)[1], (1+x^fm[i, 1])^fm[i, 2]); for(k=0, n, if(polcoeff(p^k, n)!=0, return(k)))
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Franklin T. Adams-Watters, Aug 29 2009
STATUS
approved