A383031 Indices of the squarefree terms in the sequence of exponentially odd numbers.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78

Offset: 1

Author

Amiram Eldar, Apr 13 2025

Keywords

• nonn
• easy

Comments

The asymptotic density of this sequence is A059956/A065463 = Product_{p prime} (1 - 1/(p^3 + p^2 - p)) = 0.86299074784... .

Links

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

Crossrefs

Cf. A005117, A059956, A065463, A268335, A383030.

Programs

Mathematica

expOddQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], OddQ]; Position[Select[Range[120], expOddQ], _?SquareFreeQ, Heads -> False] // Flatten

PARI

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

Formula

A268335(a(n)) = A005117(n).