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A224907 Numbers n such that the sum of reciprocals of even divisors of n > 1. 2
24, 36, 40, 48, 60, 72, 80, 84, 96, 108, 112, 120, 132, 140, 144, 156, 160, 168, 176, 180, 192, 200, 204, 208, 216, 224, 228, 240, 252, 264, 276, 280, 288, 300, 312, 320, 324, 336, 348, 352, 360, 372, 384, 392, 396, 400, 408, 416, 420, 432, 440, 444, 448, 456 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers n such that the sum of reciprocals of even divisors of n equals m/n for some integer m where the fraction m/n > 1. The corresponding numerators m are given by the sequence A204822(n) = {28, 39, 42, 60, 72, 91, 90, 96,...} (Sum of divisors (A000203) of abundant numbers (A005101).
LINKS
FORMULA
a(n) = 2*A005101(n).
EXAMPLE
40 is in the sequence because the even divisors of 40 are 2, 4, 8 , 10, 20, 40 and 1/2 + 1/4 + 1/8 + 1/10 + 1/20 + 1/40 = 42/40 = A204823(3)/a(3), and 42/40 > 1.
MAPLE
***program 1 where sum of reciprocals even divisors > 1***
with(numtheory):for n from 2 by 2 to 500 do:x:=divisors(n):n1:=nops(x): s:=0:for i from 1 to n1 do: if irem(x[i], 2)=0 then s:=s+1/x[i]:else fi:od: if s>1 then printf(`%d, `, n):else fi:od:
***program 2 where sum of reciprocals even divisors = m/n***
with(numtheory):for n from 2 to 500 do:x:=divisors(n):n1:=nops(x): s:=0:for i from 1 to n1 do: if irem(x[i], 2)=0 then s:=s+1/x[i]:else fi:od: for m from n+1 to 2*n do: if s=m/n then printf(`%d, `, n):else fi:od:od:
MATHEMATICA
Select[Range[500], Total[1/Select[Divisors[#], EvenQ]]>1&] (* Harvey P. Dale, Aug 15 2015 *)
CROSSREFS
Sequence in context: A090440 A091192 A067807 * A292352 A307342 A067341
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 25 2013
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)