cp's OEIS Frontend

A100577 Number of sets of divisors of n with an odd sum.

%I A100577 #19 Feb 13 2018 10:05:43
%S A100577 1,2,2,4,2,8,2,8,4,8,2,32,2,8,8,16,2,32,2,32,8,8,2,128,4,8,8,32,2,128,
%T A100577 2,32,8,8,8,256,2,8,8,128,2,128,2,32,32,8,2,512,4,32,8,32,2,128,8,128,
%U A100577 8,8,2,2048,2,8,32,64,8,128,2,32,8,128,2,2048,2,8,32,32,8,128,2,512,16,8,2
%N A100577 Number of sets of divisors of n with an odd sum.
%C A100577 a(n) = A000079(A032741(n)).
%C A100577 Also number of subsets of divisors of n which do not contain 1; thus a(n) = (A100587(n)+1)/2. - _Vladeta Jovovic_, Jul 02 2007
%H A100577 Antti Karttunen, <a href="/A100577/b100577.txt">Table of n, a(n) for n = 1..10000</a>
%F A100577 a(n) = 2^(A000005(n)-1).
%e A100577 a(12) = #{{1}, {3}, {1,2}, {1,4}, {2,3}, {1,6}, {3,4}, {1,2,4}, {3,6}, {1,2,6}, {2,3,4}, {1,4,6}, {2,3,6}, {1,12}, {3,4,6}, {1,2,4,6}, {3,12}, {1,2,12}, {2,3,4,6}, {1,4,12}, {2,3,12}, {1,6,12}, {3,4,12}, {1,2,4,12}, {3,6,12}, {1,2,6,12}, {2,3,4,12}, {1,4,6,12}, {2,3,6,12}, {1,2,4,6,12}, {3,4,6,12}, {2,3,4,6,12}} = 32.
%p A100577 A100577 := proc(n)
%p A100577     2^(numtheory[tau](n)-1) ;
%p A100577 end proc:
%p A100577 seq(A100577(n),n=1..100) ; # _R. J. Mathar_, Nov 10 2017
%t A100577 Table[2^(DivisorSigma[0, n] - 1), {n, 1, 100}] (* _Jean-François Alcover_, Feb 13 2018 *)
%o A100577 (PARI) a(n)=2^(numdiv(n)-1) \\ _Charles R Greathouse IV_, Jan 19 2017
%Y A100577 Cf. A000005, A000079, A001227, A032741, A100587.
%K A100577 nonn,easy
%O A100577 1,2
%A A100577 _Reinhard Zumkeller_, Nov 29 2004