A054041 -id:A054041 - cp's OEIS frontend

A056813 Largest non-unitary prime factor of LCM(1,...,n); that is, the largest prime which occurs to power > 1 in prime factorization of LCM(1,..,n).

1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Labos Elemer, Aug 28 2000

For n>0, prime(n) appears {(prime(n+1))^2 - (prime(n))^2} times [from n=(prime(n))^2 to n=(prime(n+1))^2 - 1], that is, A000040(n) appears A069482(n) times (from n=A001248(n) to n=A084920(n+1)). - Lekraj Beedassy, Mar 31 2005
a(n) is the largest prime factor of A045948(n). [Matthew Vandermast, Oct 29 2008]
Alternative definition: a(n) = largest prime <= sqrt(n) (considering 1 as prime for this occasion, see A008578 for the 19th century definition of primes). - Jean-Christophe Hervé, Oct 29 2013

			The j-th prime appears at the position of its square, at n = prime(j)^2.

Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000

Cf. A054041, A056170.

Cf. A000040, A001248, A008578, A069482.

Table[f = Transpose[FactorInteger[LCM @@ Range[n]]]; pos = Position[f[[2]], ?(# > 1 &)]; If[pos == {}, 1, f[[1, pos[[-1]]]][[1]]], {n, 100}] (* _T. D. Noe, Oct 30 2013 *)

a(n) = prime(w) if prime(w)^2 <= n < prime(w+1)^2.

To get the sequence, repeat 1 three times, and then for any k >= 1, repeat A000040(k) A069482(k) times; or equivalently, for any k >= 1, repeat A008578(k) a number of times equal to A008578(k+1)^2 - A008578(k)^2. - Jean-Christophe Hervé, Oct 29 2013

Corrected offset by Jean-Christophe Hervé, Oct 29 2013

A231405 Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.

Original entry on oeis.org

1, 1, 3, 4, 6, 8, 10, 12, 15, 17, 20, 23, 25, 28, 32, 35, 38, 41, 45, 49, 52, 56, 60, 64, 68, 72, 76, 81, 85, 89, 94, 98, 103, 108, 113, 117, 122, 127, 132, 138, 143, 148, 153, 159, 164, 170, 175, 181, 187, 192, 198, 204, 210, 216, 222, 228, 234, 240, 247, 253

Offset: 0

Carmine Suriano, Nov 08 2013

nonn

			a(7)=12 since Sum_{i=1..12} 1/i^(1/3) = 7.106248... and Sum_{i=1..11} 1/i^(1/3) = 6.669458... .

Sela Fried, On the partial sums of the Zeta function Sum_{n>=1} 1/n^s for 0 < s < 1, 2024.

Cf. A004080, A054040, A054041 (condition >n).

Cf. A067086.

s=0;n=1;
for (i=1;i<30;i++) {
s+=1/Math.pow(i,1/3);
if (s>=n) {n++;document.write(Math.floor(i)+", ");}
}

s = 0; i = 0; Table[i++; While[s = s + 1/(i^(1/3)); s < n, i++]; i, {n, 100}] (* T. D. Noe, Nov 09 2013 *)
Module[{nn=300,c},c=Accumulate[1/Surd[Range[nn],3]];Table[Position[ c,?(#>=n&),1,1],{n,0,60}]]//Flatten (* _Harvey P. Dale, Aug 14 2021 *)

a(0) added by Jon Perry, Nov 10 2013

cp's OEIS Frontend

A056168 Duplicate of A054041.

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A056813 Largest non-unitary prime factor of LCM(1,...,n); that is, the largest prime which occurs to power > 1 in prime factorization of LCM(1,..,n).

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A231405 Least integer j such that Sum_{i=1..j} 1/i^(1/3) >= n.

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