A330153 Nearest integer to the product of all integer roots of n from the second to the n-th.

1, 1, 2, 4, 8, 13, 22, 36, 56, 85, 127, 186, 268, 381, 533, 736, 1004, 1355, 1811, 2397, 3146, 4095, 5289, 6783, 8641, 10938, 13763, 17222, 21435, 26544, 32713, 40132, 49021, 59631, 72251, 87212, 104890, 125715, 150175, 178823, 212284, 251266, 296563, 349072, 409799, 479870, 560547, 653240, 759520

Offset

1,3

Links

Table of n, a(n) for n=1..49.

Formula

a(n) = round(n^(1/n)*n^(1/(n-1))*...*n^(1/2)).

a(n) = round(n^(H(n)-1)), where H(n) = A001008(n)/A002805(n).

Example

a(2) = 1 because 2^(1/2) = 1.4142...
a(3) = 2 because 3^(1/2)*3^(1/3) = 1.7320508... * 1.44224957... = 2.49804953243...

Mathematica

Array[Round[# ^ (HarmonicNumber[#] - 1)] &, 38] (* Amiram Eldar, Dec 05 2019 *)

Prog

(JavaScript)
var irlist = [];
for (var i = 2; i < 40; i++) {
  var h = 1;
  for (var g = 2; g <= i; g++) {
    h = h*Math.pow(i, 1/g);
  }
  appendItem(irlist, Math.round(h));
}
console.log(irlist);
(PARI) H(n) = sum(i=1, n, 1/i);
a(n) = round(n^(H(n)-1)); \\ Michel Marcus, Dec 05 2019

Crossrefs

Cf. A001008, A002805, A067038.

Sequence in context: A144119 A207033 A291553 * A244985 A164413 A164441

Adjacent sequences: A330150 A330151 A330152 * A330154 A330155 A330156

Keyword

nonn

Author

Sebastian F. Orellana, Dec 03 2019

Status

approved