

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^21))) = 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



