A322416 The number of exponentially odd numbers <= 10^n.

1, 8, 70, 707, 7055, 70457, 704464, 7044494, 70444319, 704442438, 7044422480, 70444221328, 704442203955, 7044422015237, 70444220112432, 704442201023926, 7044422010045871

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Eckford Cohen, Arithmetical functions associated with the unitary divisors of an integer, Mathematische Zeitschrift, Vol. 74, Vol. 1 (1960), pp. 66-80.

Aleksandar Ivic, A convolution theorem with applications to some divisor functions, Publications de l'Institut Mathématique, Vol. 24, No. 38 (1978), pp. 67-78.

D. Suryanarayana and R. Sita Rama Chandra Rao, Distribution of unitarily k-free integers, Journal of the Australian Mathematical Society, Vol. 20, No. 2 (1975), pp. 129-141.

Formula

Lim_{n->oo} a(n)/10^n = 0.704442... (A065463).

Mathematica

c=0; n=0; s={}; Do[If[k > 10^n, AppendTo[s, c]; n++]; If[AllTrue[Last /@ FactorInteger[k], OddQ], c++], {k, 1, 10^6}]; s

Crossrefs

Cf. A065463, A268335.

Sequence in context: A152263 A142986 A123511 * A287482 A053729 A266433

Adjacent sequences: A322413 A322414 A322415 * A322417 A322418 A322419

Keyword

nonn,more

Author

Amiram Eldar, Aug 28 2019

Extensions

a(10)-a(16) added by Seth A. Troisi, Sep 01 2022

Status

approved