A374460 - OEIS

%I #8 Jul 10 2024 09:37:39

%S 7,18,20,24,31,39,41,63,69,74,86,89,91,97,98,109,115,121,131,135,154,

%T 161,167,174,177,179,189,194,200,211,212,223,234,243,244,249,250,265,

%U 266,268,273,290,296,302,314,325,328,338,343,348,350,366,367,373,382,388,393

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

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

%H Amiram Eldar, <a href="/A374460/b374460.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

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

%o (PARI) isexpodd(k) = {my(e = factor(k)[, 2]); for(i = 1, #e, if(!(e[i] % 2), return(0))); 1;}

%o lista(kmax) = {my(f, c = 0); for(k = 1, kmax, if(isexpodd(k), c++; if(!issquarefree(k), print1(c, ", "))));}

%Y Cf. A005117, A059956, A065463, A268335.

%Y Similar sequences: A361936, A363189, A371186, A371188.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 09 2024