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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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A000203, A005101, A204822, A224832, A225241.

Sequence in context: A090440 A091192 A067807 * A292352 A307342 A067341

Adjacent sequences:  A224904 A224905 A224906 * A224908 A224909 A224910

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jul 25 2013

STATUS

approved

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Last modified July 5 03:05 EDT 2020. Contains 335457 sequences. (Running on oeis4.)