A124438 Numbers that are not divisible by at least one of the (positive) exponents in their prime factorization.

8, 9, 25, 32, 40, 45, 49, 56, 63, 64, 75, 81, 88, 96, 99, 104, 117, 121, 125, 128, 136, 147, 152, 153, 162, 169, 171, 175, 184, 200, 207, 224, 225, 232, 243, 245, 248, 250, 261, 275, 279, 280, 288, 289, 296, 315, 320, 325, 328, 333, 343, 344, 352, 361, 363

Offset

1,1

Comments

Except for 1, every member of A124184 is in this sequence. Also, this sequence does not contain any squarefree numbers.

Define d(k) = denominator(k/A072411(k)) and f(k) = 0 if gcd(k, d(k)) > 1 or if d(k) is not squarefree, and f(k) = g(k*d(k))/d(k) otherwise, where g(k) = Product_{prime p | k} p/(p+1). Then, the asymptotic density of this sequence is 1 - (1/zeta(2)) * Sum_{k>=1} f(A001694(k))/A001694(k) = 0.1529622... . - Amiram Eldar, Oct 07 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Mathematica

Select[Range[400], MemberQ[Divisible[#, FactorInteger[#][[All, 2]]], False]&] (* Harvey P. Dale, Mar 25 2018 *)

Prog

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

Crossrefs

Cf. A001694, A072411, A124184.

Sequence in context: A115645 A068435 A302554 * A124184 A062307 A114130

Adjacent sequences: A124435 A124436 A124437 * A124439 A124440 A124441

Keyword

nonn,easy

Author

Franklin T. Adams-Watters, Dec 16 2006

Status

approved