A sequence S describing its partial sums

[franktaw at netscape.net]

The similar sequence for partial products starts:

1,2,4,8,6,384,9,64,1327104,11,1239888338878464,13,
19985200207528358174805718990848,15,
5991123410024872959874109356233638881758664906129756792616386560,
17,
6101905151405170547540546026693263172757580912818699085074146905224294718
51566282216960532914796625991381717384814378332926771200,
19

These are much simpler when factored; for example,
a(17) - the big number between 17 and 19 - is
2^272*3^66*5^2*11^8*13^4*17.

Franklin T. Adams-Watters


-----Original Message-----
From: Max A. <maxale at gmail.com>

On 8/14/06, franktaw at netscape.net <franktaw at netscape.net> wrote: 
 
> a(a(n)) = sum_{k=1}^n a(k) 
 
The first 100 terms of the sequence S are: 
 
1, 3, 4, 8, 6, 22, 9, 16, 53, 11, 133, 13, 279, 15, 573, 69, 18, 1233, 
20, 2486, 23, 44, 4995, 25, 10059, 27, 20145, 29, 40319, 31, 80669, 
33, 161371, 35, 322777, 37, 645591, 39, 1291221, 41, 2582483, 43, 
5165009, 5039, 46, 10335103, 48, 20670254, 50, 41340558, 52, 82681168, 
122, 55, 165362513, 57, 330725083, 59, 661450225, 61, 1322900511, 63, 
2645801085, 65, 5291602235, 67, 10583204537, 70, 1215, 21166409144, 
72, 42332819575, 74, 84665639224, 76, 169331278524, 78, 338662557126, 
80, 677325114332, 82, 1354650228746, 84, 2709300457576, 86, 
5418600915238, 88, 10837201830564, 90, 21674403661218, 92, 
43348807322528, 94, 86697614645150, 96, 173395229290396, 98, 
346790458580890, 100, 693580917161880 
 
Max