

A126594


Floor of the average of the prime factors of n with multiplicity.


0



2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 4, 4, 2, 17, 2, 19, 3, 5, 6, 23, 2, 5, 7, 3, 3, 29, 3, 31, 2, 7, 9, 6, 2, 37, 10, 8, 2, 41, 4, 43, 5, 3, 12, 47, 2, 7, 4, 10, 5, 53, 2, 8, 3, 11, 15, 59, 3, 61, 16, 4, 2, 9, 5, 67, 7, 13, 4, 71, 2, 73, 19, 4, 7, 9, 6, 79, 2, 3, 21, 83, 3, 11, 22, 16, 4, 89, 3, 10
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OFFSET

2,1


LINKS

Table of n, a(n) for n=2..91.


FORMULA

a(p^n)=p, p prime, n>=1 . [From Philippe Deléham, Nov 23 2008]
a(n)=Floor(A001414(n)/A001222(n)). [From Philippe Deléham, Nov 24 2008]


MATHEMATICA

Table[Floor[(Plus@@Times@@@FactorInteger[n])/PrimeOmega[n]], {n, 2, 90}] (* Alonso del Arte, May 21 2012 *)


PROG

(PARI) avg(n) = { local(x, j, ln) for(x=2, n, a=ifactor(x); ln=length(a); print1(floor(sum(j=1, ln, a[j])/ln)", ")) } ifactor(n) = \The vector of the prime factors of n with multiplicity. { local(f, j, k, flist); flist=[]; f=Vec(factor(n)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }


CROSSREFS

Cf. A067629 (rounding instead of flooring), A076690.
Sequence in context: A079866 A134332 A080210 * A086765 A079868 A088444
Adjacent sequences: A126591 A126592 A126593 * A126595 A126596 A126597


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Jan 06 2007


STATUS

approved



