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

Author

T. D. Noe, May 23 2012

Keywords

• nonn

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

Crossrefs

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

Cf. A212610 (primitive pairs).

Programs

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]] &]