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

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, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15

Offset

1,2

Comments

a(n) = partial sums of A053866(n-1) and A093709(n-1). - Jaroslav Krizek, Oct 18 2009

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

References

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

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

a(n) = floor(sqrt(n)) + floor(sqrt(n/2)). (Crandall and Pomerance). - Franz Vrabec, Jun 24 2006

Mathematica

Accumulate[If[OddQ[DivisorSigma[1, #]], 1, 0]&/@Range[90]] (* Harvey P. Dale, Jul 15 2012 *)

Prog

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

Crossrefs

Cf. A000203, A028982, A053866, A093709.

Sequence in context: A078571 A362970 A194343 * A358472 A004788 A284523

Adjacent sequences: A071857 A071858 A071859 * A071861 A071862 A071863

Keyword

easy,nonn

Author

Benoit Cloitre, Jun 09 2002

Extensions

Offset corrected by Amiram Eldar, May 21 2022

Status

approved