OFFSET
1,1
COMMENTS
This sequence is a subsequence of A194771. The sequence A139256 (twice even perfect numbers) is a subsequence and the sum of the reciprocals of even divisors equals 1 (see the proof in this sequence). But, for the non-twice even perfect numbers of this sequence, for example a(5) = 60480, a(6) = 65520, a(7) = 4357080 so the sum of the reciprocals of even divisors equals 2.
Conjecture: if a(n) is a non-twice even perfect numbers, the sum of reciprocals of even divisors equals 2.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1013
FORMULA
a(n) = 2*A325637(n). - Amiram Eldar, Jun 26 2024
EXAMPLE
MAPLE
with(numtheory):for n from 2 to 200000 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>0 and s=floor(s) then print(n):else fi:od:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 21 2013
EXTENSIONS
a(17)-a(23) from Amiram Eldar, Jun 26 2024
STATUS
approved