A329728 - OEIS

%I #12 May 19 2020 03:28:34

%S 1,4,8,9,15,27,35,36,37,55,67,71,85,109,133,134,152,155,175,181,213,

%T 249,273,277,278,320,321,329,359,431,463,464,512,566,614,615,653,713,

%U 769,775,817,913,957,969,975,1047,1095,1099,1100,1103,1175,1189,1243

%N Partial sums of A092261.

%D Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 50.

%H Amiram Eldar, <a href="/A329728/b329728.txt">Table of n, a(n) for n = 1..10000</a>

%H Eckford Cohen, <a href="http://dx.doi.org/10.1007/BF01180473">Arithmetical functions associated with the unitary divisors of an integer</a>, Mathematische Zeitschrift, Vol. 74, No. 1 (1960), pp. 66-80.

%H Steven R. Finch, <a href="/A007947/a007947.pdf">Unitarism and Infinitarism</a>, February 25, 2004. [Cached copy, with permission of the author]

%H Vaclav Kotesovec, <a href="/A329728/a329728.jpg">Plot of a(n)/n^2 for n = 1..1000000</a>

%F Lim_{n->oo} a(n)/n^2 = 1/2 * Product_{p prime}(1 - 1/(p^2*(p+1))) = 1/2 * A065465.

%t Accumulate[Table[Plus @@ Select[Divisors@ n, Max @@ Last /@ FactorInteger@ # == 1 && GCD[#, n/#] == 1 &], {n, 1, 53}]] (* after _Michael De Vlieger_ at A092261 *)

%Y Cf. A065465, A092261.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 19 2019