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%I #57 May 04 2023 20:37:51
%S 1,1,2,4,8,13,22,36,56,85,127,186,268,381,533,736,1004,1355,1811,2397,
%T 3146,4095,5289,6783,8641,10938,13763,17222,21435,26544,32713,40132,
%U 49021,59631,72251,87212,104890,125715,150175,178823,212284,251266,296563,349072,409799,479870,560547,653240,759520
%N Nearest integer to the product of all integer roots of n from the second to the n-th.
%F a(n) = round(n^(1/n)*n^(1/(n-1))*...*n^(1/2)).
%F a(n) = round(n^(H(n)-1)), where H(n) = A001008(n)/A002805(n).
%e a(2) = 1 because 2^(1/2) = 1.4142...
%e a(3) = 2 because 3^(1/2)*3^(1/3) = 1.7320508... * 1.44224957... = 2.49804953243...
%t Array[Round[# ^ (HarmonicNumber[#] - 1)] &, 38] (* _Amiram Eldar_, Dec 05 2019 *)
%o (JavaScript)
%o var irlist = [];
%o for (var i = 2; i < 40; i++) {
%o var h = 1;
%o for (var g = 2; g <= i; g++) {
%o h = h*Math.pow(i,1/g);
%o }
%o appendItem(irlist,Math.round(h));
%o }
%o console.log(irlist);
%o (PARI) H(n) = sum(i=1, n, 1/i);
%o a(n) = round(n^(H(n)-1)); \\ _Michel Marcus_, Dec 05 2019
%Y Cf. A001008, A002805, A067038.
%K nonn
%O 1,3
%A _Sebastian F. Orellana_, Dec 03 2019
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