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A071860 Number of k 1<=k<=n such that sigma(k) is odd. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

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

R. Crandall, C. Pomerance, Prime numbers: a computational perspective. Springer-Verlag, New York, 2001, p. 52.

LINKS

Table of n, a(n) for n=2..82.

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, 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. A028982.

Sequence in context: A055656 A078571 A194343 * A004788 A284523 A034584

Adjacent sequences:  A071857 A071858 A071859 * A071861 A071862 A071863

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Jun 09 2002

STATUS

approved

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Last modified September 27 13:39 EDT 2020. Contains 337380 sequences. (Running on oeis4.)