

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
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OFFSET

1,1


COMMENTS

These are pairs of friendly deficient numbers. The terms a(2k) are in order, but terms a(2k1) may be out of order. It appears that a deficient number n can have at most one other number m such that sigma(n)/n = sigma(m)/m. Note that all known terms are odd.
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.


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: A225360 A328651 A159201 * A212610 A336554 A238330
Adjacent sequences: A211677 A211678 A211679 * A211681 A211682 A211683


KEYWORD

nonn


AUTHOR

T. D. Noe, May 23 2012


STATUS

approved



