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Search: id:A164879
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| A164879 |
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Maximum number of copies of unique prime divisors of n required to express n as a sum; a(1) = 0 by convention. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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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.
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EXAMPLE
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For n = 12, the sum 2+2+2+3+3 uses each prime factor at most 3 times, so a(12) = 3.
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PROGRAM
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(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)))
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CROSSREFS
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Cf. A164878, A164880, A027748.
Sequence in context: A030767 A135545 A123317 this_sequence A009195 A072994 A052126
Adjacent sequences: A164876 A164877 A164878 this_sequence A164880 A164881 A164882
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KEYWORD
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nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 29 2009
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