cp's OEIS Frontend

A261447 The number of distinct prime factors of the number of proper divisors of n.

%I A261447 #15 Aug 20 2015 14:34:41
%S A261447 0,0,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,
%T A261447 1,0,1,1,1,0,1,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,0,1,1,2,1,1,0,1,1,
%U A261447 1,0,1,0,1,1,1,1,1,0,1,1,1
%N A261447 The number of distinct prime factors of the number of proper divisors of n.
%C A261447 Starts to differ from A174889 at n=64.
%C A261447 The first 2 occurs at n = 64, the first 3 at n = 1081080.
%C A261447 The first 4 occurs at n = 75424789440 and the first 5 occurs at 2474044411193114760000. - _Charles R Greathouse IV_, Aug 20 2015
%H A261447 Charles R Greathouse IV, <a href="/A261447/b261447.txt">Table of n, a(n) for n = 2..10000</a>
%H A261447 L. Troupe, <a href="http://dx.doi.org/10.1016/j.jnt.2014.11.014">On the number of prime factors of values of the sum-of-proper-divisors function</a>, J. Number Theory 150 (2015)120-135
%F A261447 a(n) = A001221(A032741(n)).
%p A261447 A261447 := proc(n)
%p A261447         A001221(A032741(n)) ;
%p A261447 end proc:
%t A261447 PrimeNu[DivisorSigma[0,#]-1&/@Range[2,82]] (* _Ivan N. Ianakiev_, Aug 20 2015 *)
%o A261447 (PARI) a(n)=omega(numdiv(n)-1) \\ _Charles R Greathouse IV_, Aug 20 2015
%Y A261447 Cf. A001221, A032741, A007416, A002182.
%K A261447 nonn
%O A261447 2,63
%A A261447 _R. J. Mathar_, Aug 19 2015