A320965 Squares divisible by a single cube > 1.

16, 81, 144, 324, 400, 625, 784, 1936, 2025, 2401, 2500, 2704, 3600, 3969, 4624, 5625, 5776, 7056, 8100, 8464, 9604, 9801, 13456, 13689, 14641, 15376, 15876, 17424, 19600, 21609, 21904, 22500, 23409, 24336, 26896, 28561, 29241, 29584, 30625, 35344, 39204, 41616, 42849

Offset

1,1

Comments

Numbers whose prime factorization has a single exponent that is equal to 4 and all the rest, if they exist, are equal to 2. - Amiram Eldar, Jun 25 2022

Links

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

Formula

From Amiram Eldar, Jun 25 2022: (Start)

a(n) = A060687(n)^2.

Sum_{n>=1} 1/a(n) = (15/Pi^2) * Sum_{k>=2} (-1)^k * P(2*k) = 0.09603403868516162554..., where P(s) is the prime zeta function. (End)

Mathematica

sdscQ[n_]:=Count[Rest[Divisors[n]], _?(IntegerQ[Surd[#, 3]]&)]==1; Select[ Range[ 250]^2, sdscQ] (* Harvey P. Dale, Aug 18 2020 *)
q[n_] := (e = Sort[FactorInteger[n][[;; , 2]], Greater])[[1]] == 4 && AllTrue[Rest[e], # == 2 &]; Select[Range[200]^2, q] (* Amiram Eldar, Jun 25 2022 *)

Crossrefs

Cf. A000290, A000578, A046099, A060687, A062320, A216427, A320966, A321070.

Sequence in context: A359784 A346484 A065771 * A295071 A223951 A041490

Adjacent sequences: A320962 A320963 A320964 * A320966 A320967 A320968

Keyword

nonn

Author

Hugo Pfoertner, Oct 25 2018

Status

approved