cp's OEIS Frontend

A211677 First number k whose value of sigma(k)/k appears n times.

%I A211677 #30 Feb 16 2025 08:33:17
%S A211677 1,28,496,1638,24384,2886100,13035330,29410290,4426793280
%N A211677 First number k whose value of sigma(k)/k appears n times.
%C A211677 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 A211677 a(10) <= 27477725184. a(11) <= 88071903612. a(12) <= A027687(12). - _Donovan Johnson_, Aug 06 2012
%C A211677 For n>1, these are the smallest numbers to appear consecutively (n-1) times in A050973. - _Michel Marcus_, Jan 28 2014
%H A211677 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 A211677 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">Multiply Perfect Numbers</a> (sigma(k)/k is an integer)
%H A211677 Tom De Medts, <a href="http://mathoverflow.net/questions/56376">MathOverflow: Recovering n from sigma(n)/n</a>
%H A211677 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 A211677 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/FriendlyNumber.html">Friendly number</a>
%H A211677 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/FriendlyPair.html">Friendly pair</a>
%H A211677 Wikipedia, <a href="http://en.wikipedia.org/wiki/Friendly_number">Friendly number</a>
%e A211677 These are the values of k such that sigma(k)/k appears n times:
%e A211677 n   k values
%e A211677 1:  1
%e A211677 2:  6, 28
%e A211677 3:  6, 28, 496
%e A211677 4:  84, 270, 1488, 1638
%e A211677 5:  84, 270, 1488, 1638, 24384
%e A211677 6:  210, 17360, 43400, 284480, 2229500, 2886100
%e A211677 7:  3780, 66960, 167400, 406224, 1097280, 6656832, 13035330
%e A211677 8:  3780, 66960, 167400, 406224, 1097280, 6656832, 13035330, 29410290
%e A211677 9:  164989440, 270138960, 318729600, 326781000, 481572000, 623397600, 675347400, 995248800, 4426793280 - _Donovan Johnson_, Aug 06 2012
%e A211677 These numbers appear in A211679.
%Y A211677 Cf. A000203 (sigma), A050973, A211679.
%K A211677 nonn,hard,more
%O A211677 1,2
%A A211677 _T. D. Noe_, May 09 2012
%E A211677 a(7)-a(8) from _Donovan Johnson_, May 10 2012
%E A211677 a(9) from _Michel Marcus_ and _Donovan Johnson_, Aug 06 2012