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Partial sums of A002322.
6

%I #23 Dec 27 2022 02:27:42

%S 1,2,4,6,10,12,18,20,26,30,40,42,54,60,64,68,84,90,108,112,118,128,

%T 150,152,172,184,202,208,236,240,270,278,288,304,316,322,358,376,388,

%U 392,432,438,480,490,502,524,570,574,616,636,652,664,716,734,754,760,778

%N Partial sums of A002322.

%H G. C. Greubel, <a href="/A162578/b162578.txt">Table of n, a(n) for n = 1..10000</a>

%H Paul Erdős, Carl Pomerance, and Eric Schmutz, <a href="https://doi.org/10.4064/aa-58-4-363-385">Carmichael's lambda function</a>, Acta Arithmetica, Vol. 58, No. 4 (1991), pp. 363-385; <a href="https://math.dartmouth.edu/~carlp/PDF/lambda.pdf">alternative link</a>.

%F a(n) = Sum_{k=1..n} A002322(k).

%F a(n) = (n^2/log(n)) * exp(B * (log(log(n))/log(log(log(n)))) * (1 + o(1))), where B = A218342 (Erdős et al., 1991). - _Amiram Eldar_, Dec 27 2022

%p read("transforms3") ; a002322 := BFILETOLIST("b002322.txt") : A162578 :=proc(n) global a002322 ; local i; add(op(i,a002322),i=1..n) ; end: seq(A162578(n),n=1..120) ; # _R. J. Mathar_, Jul 16 2009

%t Accumulate[CarmichaelLambda[Range[60]]] (* _Harvey P. Dale_, Sep 21 2011 *)

%o (PARI) a(n) = sum(i=1, n, lcm(znstar(i)[2])) \\ _Felix Fröhlich_, Jul 04 2018

%Y Cf. A002322, A218342.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jul 06 2009

%E a(13) corrected and more terms added by _R. J. Mathar_, Jul 16 2009