A376173 Numbers whose prime factorization has an odd minimum exponent that is larger than 1.

8, 27, 32, 125, 128, 216, 243, 343, 432, 512, 648, 864, 1000, 1331, 1728, 1944, 2000, 2048, 2187, 2197, 2744, 3125, 3375, 3456, 4000, 4913, 5000, 5488, 5832, 6859, 6912, 7776, 8000, 8192, 9261, 10125, 10648, 10976, 12167, 13824, 15552, 16000, 16807, 16875, 17496

Offset

1,1

Comments

Numbers k such that A051904(k) is odd and larger than 1.

The minimum exponent in the prime factorization of 1 is considered to be A051904(1) = 0, and therefore 1 is not a term of this sequence.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to powerful numbers.

Formula

Sum_{n>=1} 1/a(n) = -1 + Sum_{k>=2} (-1)^k * s(k) = 0.2379998147971880759099..., where s(k) = Product_{p prime} (1 + 1/(p^k*(p-1))).

Mathematica

seq[lim_] := Select[Union@ Flatten@ Table[i^2 * j^3, {j, 1, Surd[lim, 3]}, {i, 1, Sqrt[lim/j^3]}], # > 1 && OddQ[Min[FactorInteger[#][[;; , 2]]]] &]; seq[10000]

Prog

(PARI) is(k) = {my(f = factor(k), e = f[, 2]); #e && (ispowerful(f) && vecmin(e) % 2); }

Crossrefs

Subsequence of A036966.

Complement of A376172 within A001694.

Subsequences: A030078, A062838 \ {1}.

Cf. A051904.

Sequence in context: A377820 A116002 A339595 * A335988 A097054 A370788

Adjacent sequences: A376170 A376171 A376172 * A376174 A376175 A376176

Keyword

nonn,easy

Author

Amiram Eldar, Sep 13 2024

Status

approved