cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A212609 The larger companion to the deficient numbers in A212608.

Original entry on oeis.org

819, 6975, 9009, 13923, 15561, 18837, 23751, 25389, 30303, 33579, 35217, 38493, 40131, 43407, 48321, 49959, 54873, 58149, 59787, 64701, 67977, 72891, 79443, 82719, 84357, 87633, 89271, 90675, 92547, 99099, 104013, 107289, 112203, 113841, 118575, 122031
Offset: 1

Views

Author

T. D. Noe, May 23 2012

Keywords

Comments

These numbers are in order; their companions are not.
This is a subsequence of A095301. - Michel Marcus, Sep 28 2014

Crossrefs

Cf. A095301, A212608.

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

Original entry on oeis.org

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

Views

Author

T. D. Noe, May 23 2012

Keywords

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

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]] &]
Showing 1-2 of 2 results.

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