

A067620


a(n) = p^e, where p and e are the rounded means of the prime factors p_i and the exponents e_i, respectively, in the factorization n = p_1^e_1 * ... * p_r^e_r of n into distinct primes p_i. Each mean is rounded to the nearest integer, rounding up if there's a choice.


0



2, 3, 4, 5, 3, 7, 8, 9, 4, 11, 9, 13, 5, 4, 16, 17, 9, 19, 16, 5, 7, 23, 9, 25, 8, 27, 25, 29, 3, 31, 32, 7, 10, 6, 9, 37, 11, 8, 16, 41, 4, 43, 49, 16, 13, 47, 27, 49, 16, 10, 64, 53, 9, 8, 25, 11, 16, 59, 3, 61, 17, 25, 64, 9, 5, 67, 100, 13, 5, 71, 27, 73, 20, 16, 121, 9, 6, 79
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OFFSET

2,1


LINKS

Table of n, a(n) for n=2..79.


EXAMPLE

24 = 2^3 * 3^1. The prime factors have mean (2+3)/2 = 2 1/2, which rounds up to 3. The exponents have mean (3+1)/2 = 2. So a(24) = 3^2 = 9.


MAPLE

with(numtheory): for n from 2 to 100 do pmean := round(sum(ifactors(n)[2][i][1], i=1..nops(ifactors(n)[2]))/nops(ifactors(n)[2])): emean := round(sum(ifactors(n)[2][i][2], i=1..nops(ifactors(n)[2]))/nops(ifactors(n)[2])): printf(`%d, `, pmean^emean) od:


MATHEMATICA

a[n_] := Floor[1/2+(Plus@@First/@(fn=FactorInteger[n]))/(lth=Length[fn])]^Floor[1/2+(Plus@@Last/@fn)/lth]


CROSSREFS

Sequence in context: A081810 A071829 A229998 * A294650 A053585 A098988
Adjacent sequences: A067617 A067618 A067619 * A067621 A067622 A067623


KEYWORD

easy,nonn


AUTHOR

Joseph L. Pe, Feb 02 2002


EXTENSIONS

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


STATUS

approved



