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Number of distinct prime factors in the n-th multiply perfect number A007691(n).
5

%I #10 Apr 13 2022 19:42:35

%S 0,2,2,3,2,3,2,4,5,4,6,5,2,5,6,6,7,5,2,7,7,6,6,6,2,7,7,7,6,8,8,8,8,6,

%T 7,8,8,9,7,8,2,9,9,9,11,10,9,10,10,8,9,11,10,10,8,11,11,10,10,11,11,9,

%U 11,9,12,11,13,13,12,11,12,12,11,13,12,12,12,11,12,13,12,11,10,13,12,11,10

%N Number of distinct prime factors in the n-th multiply perfect number A007691(n).

%C If a multiply perfect number k has abundancy m = sigma(k)/k, then k must have at least A005579(m) distinct prime factors.

%H T. D. Noe, <a href="/A134740/b134740.txt">Table of n, a(n) for n=1..5000</a> (using Flammenkamp's data)

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>

%Y Cf. A007691.

%K nonn

%O 1,2

%A _T. D. Noe_, Nov 07 2007