cp's OEIS Frontend

A071860 Number of k 1<=k<=n such that sigma(k) is odd.

%I A071860 #26 May 21 2022 08:42:30
%S A071860 1,2,2,3,3,3,3,4,5,5,5,5,5,5,5,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,
%T A071860 9,10,10,10,10,10,10,10,10,10,10,10,10,10,11,12,12,12,12,12,12,12,12,
%U A071860 12,12,12,12,12,12,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,15
%N A071860 Number of k 1<=k<=n such that sigma(k) is odd.
%C A071860 a(n) = partial sums of A053866(n-1) and A093709(n-1). - _Jaroslav Krizek_, Oct 18 2009
%C A071860 a(n) = number of points in [0, n*Pi/2] where cos(x) cos(x/2) ... cos(x/n) changes sign. - _Robert Israel_, Apr 29 2011
%D A071860 Richard Crandall and Carl Pomerance, Prime numbers: a computational perspective. Springer-Verlag, New York, 2001, p. 52.
%H A071860 Amiram Eldar, <a href="/A071860/b071860.txt">Table of n, a(n) for n = 1..10000</a>
%F A071860 a(n) = floor( C * sqrt(n) ) +- 1, 0 with C = 1+1/sqrt(2) = 1.707...
%F A071860 a(n) = floor(sqrt(n)) + floor(sqrt(n/2)). (Crandall and Pomerance). - _Franz Vrabec_, Jun 24 2006
%t A071860 Accumulate[If[OddQ[DivisorSigma[1,#]],1,0]&/@Range[90]] (* _Harvey P. Dale_, Jul 15 2012 *)
%o A071860 (PARI) for(n=1,100,print1(sum(i=1,n,if(sigma(i)%2,1,0)),","))
%Y A071860 Cf. A000203, A028982, A053866, A093709.
%K A071860 easy,nonn
%O A071860 1,2
%A A071860 _Benoit Cloitre_, Jun 09 2002
%E A071860 Offset corrected by _Amiram Eldar_, May 21 2022