A020639 and A117078, sequences of weights

[reismann at free.fr]

Dear Seqfans

A020639 (Lpf(n): least prime dividing n (a(1)=1)) is the weight of natural
numbers in the decomposition in weight*level (gap=cste=0).
The numbers for which the weight is equal to 2, 3, 5... are those formed by the
sieve of Eratosthenes.
Watch the graph (log) of A020639 :
http://www.research.att.com/~njas/sequences/table?a=20639&fmt=5
level 1 = prime numbers
and now the graph (log) of A117078 (the weight of prime numbers) :
http://www.research.att.com/~njas/sequences/table?a=117078&fmt=5

The weights of even numbers in  the decomposition in weight*level+gap
(gap=cste=2) form A117871.
The weights of odd numbers in  the decomposition in weight*level+gap
(gap=cste=2) are closed to A090368.
Neil, I'll send you the b-files for A117871 and A090368. Could you draw the log
graphs ? Thank you.

For more explanations on the decomposition of natural numbers (in french) :
http://reismann.free.fr/entiers.php

Best,

Rémi EISMANN