introduction and new sequence

[Andrew Plewe]

Hello, I've recently joined the list and I'd like to introduce myself.
My name is Andrew Plewe, I work as a computer programmer in California.
I'm interested in number theory, specifically factoring and primes.  The
sequences I've submitted to the OEIS originate from my explorations of
number theory.


Here is one such sequence.  If anyone has suggestions/corrections feel
free to email them to me at aplewe at sbcglobal.net.  I plan to submit this
sequence in a couple of days:


The sequence:
1, 1, 5, 1, 6, 1, 18, 7, 10, 1, 24, 1, 13, 9, 54, 1, 31, 1, 34, 12, 21,
1, 73, 11, 25, 36, 53, 1, 47, 1, 145, 18, 34, 13, 100, 1, 37, 21, 120,
1, 54, 1, 85, 51, 44, 1, 200, 15, 70


Definition:
Sum of index values of the prime factors (counted with multiplicity) for
each positive integer greater than two.


Comment:
herein p_x denotes prime p with index value x.

This sequence is generated as follows:

P = the set of prime factors of the positive integers greater than two,
counted with multiplicity.  Order the members of this set into subsets
such that each prime has its own set with an index value assigned to
each instance of the prime.  Therefore, P = {{2_1, 2_2,..2_x}, {3_1,
3_2,..3_x}, . . {p_1, p_2,..p_x}}.  In generating the sequence, each
indexed instance of a prime can only be used once.  Starting with
integers i = 2 to i = 8, we proceed as follows:

i = 2_1,              n = 1
i = 3_1,              n = 1
i = 4 = 2_2 * 2_3,    n = 2 + 3 = 5
i = 5_1,              n = 1
i = 6 = 3_2 * 2_4,    n = 2 + 4 = 6
i = 7_1,              n = 1
i = 2_5 * 2_6 * 2_7,  n = 5 + 6 + 7 = 18

and etc.

i = 2 to i = 50 are shown.

	-Andrew Plewe-