login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A335988 Cubefull exponentially odd numbers: numbers whose prime factorization contains only odd exponents that are larger than 1. 1
1, 8, 27, 32, 125, 128, 216, 243, 343, 512, 864, 1000, 1331, 1944, 2048, 2187, 2197, 2744, 3125, 3375, 3456, 4000, 4913, 6859, 7776, 8192, 9261, 10648, 10976, 12167, 13824, 16000, 16807, 17496, 17576, 19683, 24389, 25000, 27000, 29791, 30375, 31104, 32768, 35937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is a permutation of the squares (A000290) multiplied by their squarefree kernel (A007947), i.e., the numbers of the form k^2*rad(k^2) = k^2*rad(k).

This sequence is also a permutation of the exponentially odd numbers (A268335) multiplied by the square of their squarefree kernel (A007947).

a(n)/rad(a(n)) is a permutation of the squares.

a(n)/rad(a(n))^2 is a permutation of the exponentially odd numbers.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..6000

FORMULA

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.2312911... (A065487).

EXAMPLE

8 = 2^3 is a term since the exponent of its prime factor 2 is 3 which is odd and larger than 1.

MATHEMATICA

Join[{1}, Select[Range[10^5], AllTrue[Last /@ FactorInteger[#], #1 > 1 && OddQ[#1] &] &]]

CROSSREFS

Intersection of A001694 and A268335.

Intersection of A036966 and A268335.

A030078, A050997, A092759, A179665, A079395 and A138031 are subsequences.

Cf. A000290, A007947, A065487.

Sequence in context: A262675 A102834 A116002 * A097054 A304291 A056824

Adjacent sequences:  A335984 A335985 A335986 * A335989 A335990 A335991

KEYWORD

nonn

AUTHOR

Amiram Eldar, Jul 03 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 28 12:39 EDT 2020. Contains 338055 sequences. (Running on oeis4.)