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A048978
Light numbers, those whose mean sum of divisors <= mean running sum of divisors of all previous n.
2
360, 630, 720, 840, 900, 960, 1008, 1080, 1120, 1200, 1260, 1320, 1344, 1400, 1440, 1512, 1540, 1560, 1584, 1620, 1680, 1728, 1760, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2112, 2160, 2184, 2240, 2268, 2280, 2310, 2340, 2352, 2376, 2400
OFFSET
1,1
LINKS
FORMULA
Keep running totals of sum, rs and number of divisors, rd, for all numbers to n-1. Divide rs by rd. If mean at n <= running mean at n-1, then number is "light, " else "heavy."
EXAMPLE
a(1)=360. At 360 rs/rd of all previous n is 105811/2162=48.94+. At 360, s/d is 1170/24=48.75. 48.75<=48.94 so 360 is "Light."
MATHEMATICA
t = {1, 1}; seq = {}; Do[s = DivisorSigma[#, n] & /@ {0, 1}; If[s[[2]]/s[[1]] < t[[2]]/t[[1]], AppendTo[seq, n]]; t += s, {n, 2, 2400}]; seq (* Amiram Eldar, Sep 06 2019 *)
CROSSREFS
Sequence in context: A163569 A063067 A076205 * A056502 A056492 A158308
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
a(22) corrected by Amiram Eldar, Sep 06 2019
STATUS
approved