A124184 Positive integers not divisible by any of their own prime-factorization exponents.

1, 8, 9, 25, 32, 49, 64, 81, 121, 125, 128, 169, 225, 243, 289, 343, 361, 441, 512, 529, 625, 729, 841, 961, 1000, 1024, 1089, 1225, 1331, 1369, 1521, 1681, 1849, 2025, 2048, 2187, 2197, 2209, 2401, 2601, 2744, 2809, 3025, 3249, 3481, 3721, 3969, 4096, 4225

Offset

1,2

Comments

If k > 1 is a term then k is composite and is not squarefree. - Farideh Firoozbakht, Dec 08 2006

Moreover, all the terms are powerful numbers (A001694). - Amiram Eldar, Oct 07 2025

Links

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

Example

18225 = 3^6 * 5^2. Neither 6 nor 2 divides 18225, so 18225 is in the sequence.

Mathematica

f[n_] := Times @@ Mod[n, Last /@ FactorInteger[n]] > 0; Select[Range[5000], f] (* Ray Chandler, Dec 06 2006 *)
Do[a = FactorInteger[n]; l = Length[a]; b = Table[a[[k]][[2]], {k, l}]; If[ ! MemberQ[Mod[n, b], 0], Print[n]], {n, 4000}] (* Farideh Firoozbakht, Dec 08 2006 *)

Prog

(PARI) isok(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(k % e[i]), return(0))); 1; } \\ Amiram Eldar, Oct 07 2025

Crossrefs

Cf. A001694, A124438.

Sequence in context: A068435 A302554 A124438 * A062307 A114130 A130100

Adjacent sequences: A124181 A124182 A124183 * A124185 A124186 A124187

Keyword

nonn,easy

Author

Leroy Quet, Dec 05 2006

Extensions

Extended by Ray Chandler and Zak Seidov, Dec 06 2006

Status

approved