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

1,1

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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, ", ")))); }

Crossrefs

Cf. A005117, A059956, A065463, A268335.

Similar sequences: A361936, A363189, A371186, A371188.

Sequence in context: A103570 A223247 A091832 * A256011 A272972 A070609

Adjacent sequences: A374457 A374458 A374459 * A374461 A374462 A374463

Keyword

nonn,easy

Author

Amiram Eldar, Jul 09 2024

Status

approved