

A172460


Partial sums of economical numbers A046759.


0



125, 253, 496, 752, 1095, 1607, 2232, 2961, 3985, 5014, 6229, 7479, 8759, 10090, 11459, 12917, 14453, 16134, 17835, 19550, 21342, 23191, 25066, 27114, 29301, 31498, 33707, 36108, 38668, 41477, 44602, 48083, 51667, 55312, 59033, 63129
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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?


LINKS

Table of n, a(n) for n=1..36.


FORMULA

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)}.


EXAMPLE

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.


CROSSREFS

Cf. A000961, A046758, A046759, A046760.
Sequence in context: A045199 A260604 A023079 * A338469 A253226 A223182
Adjacent sequences: A172457 A172458 A172459 * A172461 A172462 A172463


KEYWORD

base,easy,nonn


AUTHOR

Jonathan Vos Post, Feb 03 2010


STATUS

approved



