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.

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

Hugo Pfoertner, Table of n, a(n) for n = 2..10000

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

Cf. A078175, A126594.

Sequence in context: A109674 A284260 A218993 * A079870 A364156 A185642

Adjacent sequences: A067626 A067627 A067628 * A067630 A067631 A067632

Keyword

easy,nonn

Author

Joseph L. Pe, Feb 02 2002

Extensions

Edited by Dean Hickerson and James A. Sellers, Feb 12 2002

Status

approved