OFFSET
1,4
COMMENTS
For p prime, a(p^k) = p^(k-1). For p and q distinct primes, a(pq) = min(p,q).
a(n) >= n/sopf(n), where sopf is A008472; when the right hand side is an integer, this is an equality.
EXAMPLE
For n = 12, the sum 2+2+2+3+3 uses each prime factor at most 3 times, so a(12) = 3.
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]); for(k=0, n, if(polcoeff(p^k, n)!=0, return(k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Franklin T. Adams-Watters, Aug 29 2009
STATUS
approved