A071860 - OEIS

%I #26 May 21 2022 08:42:30

%S 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 9,10,10,10,10,10,10,10,10,10,10,10,10,10,11,12,12,12,12,12,12,12,12,

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

%C a(n) = partial sums of A053866(n-1) and A093709(n-1). - _Jaroslav Krizek_, Oct 18 2009

%C 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 Richard Crandall and Carl Pomerance, Prime numbers: a computational perspective. Springer-Verlag, New York, 2001, p. 52.

%H Amiram Eldar, <a href="/A071860/b071860.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = floor( C * sqrt(n) ) +- 1, 0 with C = 1+1/sqrt(2) = 1.707...

%F a(n) = floor(sqrt(n)) + floor(sqrt(n/2)). (Crandall and Pomerance). - _Franz Vrabec_, Jun 24 2006

%t Accumulate[If[OddQ[DivisorSigma[1,#]],1,0]&/@Range[90]] (* _Harvey P. Dale_, Jul 15 2012 *)

%o (PARI) for(n=1,100,print1(sum(i=1,n,if(sigma(i)%2,1,0)),","))

%Y Cf. A000203, A028982, A053866, A093709.

%K easy,nonn

%O 1,2

%A _Benoit Cloitre_, Jun 09 2002

%E Offset corrected by _Amiram Eldar_, May 21 2022