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A356005
Number of integers k such that k*tau(k) <= n.
1
1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 9, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 20, 20, 21, 22, 22, 22, 22, 22
OFFSET
1,4
COMMENTS
Partial sums of A327166. - Rémy Sigrist, Jul 23 2022
LINKS
R. Balasubramanian and K. Ramachandra, On the number of integers n such that nd(n)<=x, Acta Arith., 49 (1988), 313-322.
FORMULA
a(n) is asymptotic to C*n/sqrt(log(n)) for a suitable constant C > 0.
MATHEMATICA
Table[Sum[If[k*DivisorSigma[0, k] <= n, 1, 0], {k, 1, n}], {n, 1, 100}] (* Vaclav Kotesovec, Jul 23 2022 *)
PROG
(PARI) a(n)=sum(k=1, n, if(k*numdiv(k)<=n, 1, 0))
CROSSREFS
Sequence in context: A225633 A060960 A073642 * A262869 A342678 A108356
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jul 22 2022
STATUS
approved