A126594 Floor of the average of the prime factors of n with multiplicity.

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

Offset

2,1

Links

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

Formula

a(p^n)=p, p prime, n >= 1. - Philippe Deléham, Nov 23 2008

a(n) = floor(A001414(n)/A001222(n)). - 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.

This is the floor of A123528/A123529.

Without multiplicity we have A363895.

For prime indices instead of factors we have A363943, triangle A363945.

Positions of first appearances are A364037.

The ceiling is A364156.

Positions of 2's are A364157, for prime indices A363949.

A051293 counts subsets with integer mean, median A000975.

A067538 counts partitions with integer mean, ranks A316413.

A078175 lists numbers with integer mean of prime factors.

Cf. A026905, A326567/A326568, A327473, A327476, A363944, A363948, A363950.

Sequence in context: A276632 A273288 A080210 * A363895 A086765 A079868

Adjacent sequences: A126591 A126592 A126593 * A126595 A126596 A126597

Keyword

easy,nonn

Author

Cino Hilliard, Jan 06 2007

Status

approved