A211680 Pairs of deficient numbers having the same value of sigma(k)/k in the order that they are found.

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

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

Cf. A005100 (deficient numbers), A212608, A212609 (the pairs separated).

Cf. A212610 (primitive pairs).

Sequence in context: A328651 A159201 A362400 * A212610 A336554 A238330

Adjacent sequences: A211677 A211678 A211679 * A211681 A211682 A211683

Keyword

nonn

Author

T. D. Noe, May 23 2012

Status

approved