A164879 Maximum number of copies of unique prime divisors of n required to express n as a sum; a(1) = 0 by convention.

0, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 3, 8, 1, 4, 1, 4, 3, 2, 1, 6, 5, 2, 9, 4, 1, 3, 1, 16, 3, 2, 5, 8, 1, 2, 3, 6, 1, 4, 1, 4, 6, 2, 1, 10, 7, 8, 3, 4, 1, 12, 5, 7, 3, 2, 1, 6, 1, 2, 7, 32, 5, 5, 1, 4, 3, 5, 1, 15, 1, 2, 10, 4, 7, 5, 1, 12, 27, 2, 1, 7, 5, 2, 3, 8, 1, 9, 7, 4, 3, 2, 5, 20, 1, 12, 9, 15, 1

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.

Links

Table of n, a(n) for n=1..101.

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

Cf. A164878, A164880, A027748.

Sequence in context: A231557 A171453 A285707 * A200219 A270120 A325567

Adjacent sequences: A164876 A164877 A164878 * A164880 A164881 A164882

Keyword

nonn

Author

Franklin T. Adams-Watters, Aug 29 2009

Status

approved