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A168133 Numbers m = sum_(k=1...n) sigma(k) such that sum_(k=1...n) sigma(k) / k is integer for any k. 4
1, 4, 56, 99, 238, 3276, 26820, 55167, 550514, 3842258, 16222973, 56731455, 118396264, 396379039896, 9772829297132, 15876697439182, 2710103706735457, 4438313663247000, 12136546505785858, 3518811208764622050 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers m = A024916(k) such that A024916(k) / k is integer for any k. If a(14) exists it must be bigger than 8*10^9.

Corresponding values of k, and sum_(k=1...n) sigma(k)/k are given in A056550 and A168132. [From Jaroslav Krizek, Nov 21 2009]

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..25

EXAMPLE

Number a(3) = 56 = A024916(8) is in sequence because A024916(8) / 8 = 56 / 8 = 7 is integer for k = 8.

MAPLE

with(numtheory);

A168133:=proc(q)  local n;  a:=0;

for n from 1 to q do a:=a+sigma(n) if type(a/n, integer) then print(a); fi; od; end:

A168133 (10^10); # Paolo P. Lava, Mar 26 2013

CROSSREFS

Sequence in context: A189873 A143650 A143649 * A189864 A192845 A144138

Adjacent sequences:  A168130 A168131 A168132 * A168134 A168135 A168136

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Nov 18 2009, Dec 04 2009

STATUS

approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)