A079631 -id:A079631 - cp's OEIS frontend

A079645 Numbers j such that the integer part of the cube root of j divides j.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210

Offset: 1

Benoit Cloitre, Jan 31 2003

nonn

Concrete Mathematics Casino Problem - Winners.

			252^(1/3) = 6.316359597656... and 252/6 = 42 hence 252 is in the sequence.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, pp. 74-76.

G. C. Greubel, Table of n, a(n) for n = 1..10000
B. Cloitre, Some divisibility sequences.

Cf. A006446, A032378, A079631, A112873, A120721.

[n: n in [1..250] | n mod Floor(n^(1/3)) eq 0 ]; // G. C. Greubel, Jul 20 2023

t1:=[]; for n from 1 to 500 do t2:=floor(n^(1/3)); if n mod t2 = 0 then t1:=[op(t1),n]; fi; od: t1; # N. J. A. Sloane, Oct 29 2006

Select[Range[1000], Mod[#, Floor[Power[#, 1/3]]] == 0 &]
Select[Range[1000],Divisible[#,Floor[CubeRoot[#]]]&] (* Harvey P. Dale, Jun 19 2023 *)

[n for n in (1..250) if n%(floor(n^(1/3)))==0 ] # G. C. Greubel, Jul 20 2023

For n = (k/2)*(3*k+11) - m for some fixed m >= 0 with n > ((k-1)/2)*(3*(k-1) + 11) we have a(n) = k^3 + 3*k^2 + (3-m)*k. - Benoit Cloitre, Jan 22 2012

A321667 (3/2) * n^(2/3) rounded to nearest integer.

Original entry on oeis.org

2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27

Offset: 1

Hugo Pfoertner, Nov 16 2018

This is an approximation to the solution of the "Concrete Math Club" casino problem given in A079631.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, pp. 74-76.

Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Cf. A079631.

a[n_]:=Round[(3/2)*n^(2/3)]; Array[a, 50] (* Stefano Spezia, Nov 16 2018 *)

for(j=1,75,print1(round(1.5*j^(2/3)),", "))

for n in range(1,50): print(round((3/2)*n**(2/3)), end=', ') # Stefano Spezia, Nov 16 2018

A204330 a(n) is the number of k satisfying 1 <= k <= n and such that floor(sqrt(k)) divides k.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 7, 8, 8, 8, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 21, 22, 22, 22, 22, 22, 22, 22

Offset: 1

Benoit Cloitre, Jan 14 2012

nonn

a(n) = floor(2*sqrt(n)) + floor(sqrt(n-1)) - 1 if n belongs to A135106 otherwise a(n) = floor(2*sqrt(n)) + floor(sqrt(n-1)) - 2.

B. Cloitre, Some divisibility sequences

Cf. A006446, A079631.

Accumulate[Boole[Table[IntegerQ[n/Floor[n^(1/2)]], {n, 1, 70}]]]  (* Geoffrey Critzer, May 25 2013 *)

PARI
```
a(n)=sum(k=1,n,if(k%sqrtint(k),0,1));
```

a(n) = card{j>=1, A006446(j)<=n}.

Corrected by Geoffrey Critzer, May 25 2013

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A079645 Numbers j such that the integer part of the cube root of j divides j.

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A321667 (3/2) * n^(2/3) rounded to nearest integer.

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A204330 a(n) is the number of k satisfying 1 <= k <= n and such that floor(sqrt(k)) divides k.

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