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A074795
Number of numbers k <= n such that tau(k) == 0 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.
3
0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21
OFFSET
1,9
LINKS
L. G. Sathe, On a congruence property of the divisor function, American Journal of Mathematics, Vol. 67, No. 3 (1945), pp. 397-406.
FORMULA
a(n) is asymptotic to c*n with c = 0.26....
The constant is c = 1 - zeta(3)/zeta(2) = 1 - 6*zeta(3)/Pi^2 = 0.2692370305 ... (Sathe, 1945). - Amiram Eldar, Aug 29 2020
MATHEMATICA
Accumulate[Boole[Divisible[DivisorSigma[0, Range[90]], 3]]] (* Harvey P. Dale, Jan 11 2015 *)
PROG
(PARI) a(n)=sum(k=1, n, if(numdiv(k)%3, 0, 1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Sep 07 2002
STATUS
approved