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 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

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