A374460 Indices of the nonsquarefree terms in the sequence of exponentially odd numbers (A268335).

7, 18, 20, 24, 31, 39, 41, 63, 69, 74, 86, 89, 91, 97, 98, 109, 115, 121, 131, 135, 154, 161, 167, 174, 177, 179, 189, 194, 200, 211, 212, 223, 234, 243, 244, 249, 250, 265, 266, 268, 273, 290, 296, 302, 314, 325, 328, 338, 343, 348, 350, 366, 367, 373, 382, 388, 393

Offset: 1

Author

Amiram Eldar, Jul 09 2024

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is 1 - A059956 / A065463 = 0.13700925215474602945... .

Examples

			The first 7 exponentially odd numbers are 1, 2, 3, 5, 6, 7, and 8. A268335(7) = 8 = 3^3 is the least nonsquarefree term. Therefore a(1) = 7.
		

Links

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

Crossrefs

Cf. A005117, A059956, A065463, A268335.

Similar sequences: A361936, A363189, A371186, A371188.

Programs

Mathematica

Position[Select[Range[120], AllTrue[FactorInteger[#][[;; , 2]], OddQ] &], _?(!SquareFreeQ[#] &), Heads -> False] // Flatten

PARI

isexpodd(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] % 2), return(0))); 1;}
lista(kmax) = {my(f, c = 0); for(k = 1, kmax, if(isexpodd(k), c++; if(!issquarefree(k), print1(c, ", "))));}

Formula

A268335(a(n)) = A374459(n).