Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #29 Jul 05 2018 20:30:31
%S 1,28,496,1638,24384,2886100,13035330,29410290,4426793280
%N First number k whose value of sigma(k)/k appears n times.
%C The values of sigma(k)/k are 1, 2, 2, 8/3, 8/3, 96/35, 32/9, 32/9, 32/7. Note that these values are nondecreasing. Is that always the case? In the table below, all numbers in the same row are friendly to each other.
%C a(10) <= 27477725184. a(11) <= 88071903612. a(12) <= A027687(12). - _Donovan Johnson_, Aug 06 2012
%C For n>1, these are the smallest numbers to appear consecutively (n-1) times in A050973. - _Michel Marcus_, Jan 28 2014
%H Claude W. Anderson and Dean Hickerson, <a href="https://www.jstor.org/stable/2318325">Problem 6020: Friendly Integers</a>, Amer. Math. Monthly 84 (1977) pp. 65-66.
%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">Multiply Perfect Numbers</a> (sigma(k)/k is an integer)
%H Tom De Medts, <a href="http://mathoverflow.net/questions/56376">MathOverflow: Recovering n from sigma(n)/n</a>
%H Carl Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper13.pdf">Multiply perfect numbers, Mersenne primes and effective computability</a>, Math. Ann. 226 (1977), 195-206.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/FriendlyNumber.html">Friendly number</a>
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/FriendlyPair.html">Friendly pair</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Friendly_number">Friendly number</a>
%e These are the values of k such that sigma(k)/k appears n times:
%e n k values
%e 1: 1
%e 2: 6, 28
%e 3: 6, 28, 496
%e 4: 84, 270, 1488, 1638
%e 5: 84, 270, 1488, 1638, 24384
%e 6: 210, 17360, 43400, 284480, 2229500, 2886100
%e 7: 3780, 66960, 167400, 406224, 1097280, 6656832, 13035330
%e 8: 3780, 66960, 167400, 406224, 1097280, 6656832, 13035330, 29410290
%e 9: 164989440, 270138960, 318729600, 326781000, 481572000, 623397600, 675347400, 995248800, 4426793280 - _Donovan Johnson_, Aug 06 2012
%e These numbers appear in A211679.
%Y Cf. A000203 (sigma), A050973, A211679.
%K nonn,hard,more
%O 1,2
%A _T. D. Noe_, May 09 2012
%E a(7)-a(8) from _Donovan Johnson_, May 10 2012
%E a(9) from _Michel Marcus_ and _Donovan Johnson_, Aug 06 2012