A020639 and A117078, sequences of weights

reismann at free.fr reismann at free.fr
Mon May 7 14:46:18 CEST 2007

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 :
level 1 = prime numbers
and now the graph (log) of A117078 (the weight of prime numbers) :

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) :



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