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.

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

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: A071829 A229998 A331469 * A343253 A330741 A319677

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