OFFSET
1,1
COMMENTS
These are pairs of friendly deficient numbers. The terms a(2k) are in order, but terms a(2k-1) may be out of order.
Many of these pairs (a,b) have the property that (k*a,k*b) is another pair for some integer k. See A212610 for primitive pairs.
From Suyash Pandit, Oct 13 2023: (Start)
The first (but not smallest) even term of this sequence is n=1278316. It is friendly to m=1680705, with sigma(n)/n = sigma(m)/m = 336/169.
The first pair of even terms in this sequence is (n,m) = (366776,1581644246) with sigma(n)/n = sigma(m)/m = 720/361.
It is possible to have more than two deficient numbers with the same value of sigma(n)/n. For example, the numbers 119129783409, 217416788955, and 1318995186327 all satisfy sigma(n)/n = 3584/1891. (End)
LINKS
T. D. Noe, Table of n, a(n) for n = 1..2860
MATHEMATICA
nn = 10^5; t = DivisorSigma[1, Range[nn]]/Range[nn]; t2 = Transpose[Select[Tally[t], #[[1]] < 2 && #[[2]] > 1 &]][[1]]; Sort[Table[Flatten[Position[t, t2[[n]]]], {n, Length[t2]}], #1[[2]] < #2[[2]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, May 23 2012
STATUS
approved