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A211680 Pairs of deficient numbers having the same value of sigma(k)/k in the order that they are found. 6
135, 819, 3375, 6975, 1485, 9009, 2295, 13923, 2565, 15561, 3105, 18837, 3915, 23751, 4185, 25389, 4995, 30303, 5535, 33579, 5805, 35217, 6345, 38493, 25137, 40131, 7155, 43407, 7965, 48321, 8235, 49959, 9045, 54873, 9585, 58149, 9855, 59787, 10665, 64701 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A005100 (deficient numbers), A212608, A212609 (the pairs separated).
Cf. A212610 (primitive pairs).
Sequence in context: A328651 A159201 A362400 * A212610 A336554 A238330
KEYWORD
nonn
AUTHOR
T. D. Noe, May 23 2012
STATUS
approved

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Last modified May 28 01:34 EDT 2024. Contains 372900 sequences. (Running on oeis4.)