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A067629
The average of the prime factors of n, rounded off to the nearest integer (rounding up if there's a choice), with each factor weighted according to its frequency of occurrence in the prime factorization.
9
2, 3, 2, 5, 3, 7, 2, 3, 4, 11, 2, 13, 5, 4, 2, 17, 3, 19, 3, 5, 7, 23, 2, 5, 8, 3, 4, 29, 3, 31, 2, 7, 10, 6, 3, 37, 11, 8, 3, 41, 4, 43, 5, 4, 13, 47, 2, 7, 4, 10, 6, 53, 3, 8, 3, 11, 16, 59, 3, 61, 17, 4, 2, 9, 5, 67, 7, 13, 5, 71, 2, 73, 20, 4, 8, 9, 6, 79, 3, 3, 22, 83, 4, 11, 23, 16, 4
OFFSET
2,1
LINKS
EXAMPLE
24 = 2^3 * 3^1, so the average of the prime factors = (2 + 2 + 2 + 3)/4, which rounded = 2. So a(24) = 2.
MAPLE
with(numtheory): for n from 2 to 150 do printf(`%d, `, round(sum(ifactors(n)[2][i][1]*ifactors(n)[2][i][2], i=1..nops(ifactors(n)[2]))/sum(ifactors(n)[2][i][2], i=1..nops(ifactors(n)[2]) ) )) od:
MATHEMATICA
a[n_] := Floor[1/2+(Plus@@(Times@@#&/@(fn=FactorInteger[n])))/(Plus@@Last/@fn)]
CROSSREFS
Sequence in context: A109674 A284260 A218993 * A079870 A364156 A185642
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Feb 02 2002
EXTENSIONS
Edited by Dean Hickerson and James A. Sellers, Feb 12 2002
STATUS
approved