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%I #2 Mar 30 2012 18:40:50
%S 125,253,496,752,1095,1607,2232,2961,3985,5014,6229,7479,8759,10090,
%T 11459,12917,14453,16134,17835,19550,21342,23191,25066,27114,29301,
%U 31498,33707,36108,38668,41477,44602,48083,51667,55312,59033,63129
%N Partial sums of economical numbers A046759.
%C The subsequence of prime partial sum of economical numbers begins: 1607, 6229, 12917, 76367. The subsequence of economical partial sum of economical numbers begins: 125; what is the first nontrivial economical partial sum of economical numbers?
%F a(n) = SUM[i=1..n] {n written as a product of primes raised to powers, where D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n)<l(n)}.
%e a(41) = 125 + 128 + 243 + 256 + 343 + 512 + 625 + 729 + 1024 + 1029 + 1215 + 1250 + 1280 + 1331 + 1369 + 1458 + 1536 + 1681 + 1701 + 1715 + 1792 + 1849 + 1875 + 2048 + 2187 + 2197 + 2209 + 2401 + 2560 + 2809 + 3125 + 3481 + 3584 + 3645 + 3721 + 4096 + 4374 + 4375 + 4489 + 4802 + 4913.
%Y Cf. A000961, A046758, A046759, A046760.
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 03 2010
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