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A242925
Numbers k such that lambda(k) divides Sum_{j=1..k} lambda(j).
1
1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 15, 16, 18, 19, 20, 24, 30, 31, 34, 40, 42, 44, 60, 72, 80, 83, 130, 132, 136, 195, 208, 218, 232, 254, 258, 259, 260, 264, 272, 276, 305, 306, 408, 420, 440, 464, 504, 560, 585, 586, 594, 595, 609, 624, 636, 715, 819, 840
OFFSET
1,2
COMMENTS
Numbers k such that A162578(k)/A002322(k) = Sum_{j=1..k}A002322(j)/ A002322(k) is an integer where lambda(k) is the Carmichael lambda function (A002322).
The corresponding integers are 1, 2, 2, 3, 6, 3, 10, 4, 21, 10, 16, 17, 15, 6, 28, 76, 60, 9, 19, 98, ...
LINKS
EXAMPLE
12 is in the sequence because A162578(12)/A002322(12) = 42/2 = 21 is an integer.
MAPLE
with(numtheory):nn:=2000:for n from 1 to nn do:p:=lambda(n): s:=sum('lambda(j)', 'j'=1..n):if irem(s, p)=0 then printf(`%d, `, n):else fi:od:
MATHEMATICA
nn = 2000; sums = Accumulate[CarmichaelLambda[Range[nn]]]; Select[Range[nn], Mod[sums[[#]], CarmichaelLambda[#]] == 0 &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 26 2014
STATUS
approved