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Search: id:A067629
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| A067629 |
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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. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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2,1
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EXAMPLE
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24 = 2^3 * 3^1, so the average of the prime factors = (2 + 2 + 2 + 3)/4, which rounded = 2. So a(24) = 2.
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MAPLE
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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:
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MATHEMATICA
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a[n_] := Floor[1/2+(Plus@@(Times@@#&/@(fn=FactorInteger[n])))/(Plus@@Last/@fn)]
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CROSSREFS
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Sequence in context: A039634 A078833 A109674 this_sequence A079870 A076690 A086287
Adjacent sequences: A067626 A067627 A067628 this_sequence A067630 A067631 A067632
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KEYWORD
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easy,nonn
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AUTHOR
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Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Feb 02 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com) and James A. Sellers (sellersj(AT)math.psu.edu), Feb 12 2002
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