A371240 -id:A371240 - cp's OEIS frontend

A371239 Squarefree numbers that are zeroless in base 3 (A032924).

1, 2, 5, 7, 13, 14, 17, 22, 23, 26, 41, 43, 53, 67, 70, 71, 77, 79, 122, 130, 131, 133, 134, 149, 151, 157, 158, 161, 202, 203, 205, 206, 211, 214, 215, 229, 230, 233, 238, 239, 241, 365, 367, 373, 374, 377, 391, 394, 395, 401, 403, 445, 446, 449, 454, 455, 457

Offset: 1

Amiram Eldar, Mar 16 2024

The relative asymptotic density of this sequence within the zeroless numbers in base 3 is 27/(4*Pi^2) = 1/A214549 = 0.683917... (Banks and Shparlinski, 2004).

Amiram Eldar, Table of n, a(n) for n = 1..10000
William D. Banks and Igor E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; alternative link.

Intersection of A005117 and A032924.

Cf. A214549, A371240, A371241.

Select[Range[500], !MemberQ[IntegerDigits[#, 3], 0] && SquareFreeQ[#] &]

is(n) = vecmin(digits(n, 3)) > 0 && issquarefree(n);

A371241 Euler totient function applied to the zeroless numbers in base 3 (A032924).

Original entry on oeis.org

1, 1, 2, 4, 6, 4, 12, 6, 8, 16, 10, 22, 20, 12, 16, 40, 42, 20, 42, 20, 24, 52, 66, 32, 24, 70, 36, 60, 78, 32, 110, 60, 60, 100, 48, 130, 108, 66, 72, 148, 150, 72, 156, 78, 64, 132, 100, 168, 160, 102, 210, 104, 106, 168, 228, 88, 112, 232, 96, 238, 240, 110

Offset: 1

Amiram Eldar, Mar 16 2024

Amiram Eldar, Table of n, a(n) for n = 1..10000
William D. Banks and Igor E. Shparlinski, Arithmetic properties of numbers with restricted digits, Acta Arithmetica, Vol. 112, No. 4 (2004), pp. 313-332; alternative link.

Cf. A000010, A032924, A214549, A371239, A371240.

EulerPhi[Select[Range[300], !MemberQ[IntegerDigits[#, 3], 0] &]]

lista(kmax) = for(k = 1, kmax, if(vecmin(digits(k, 3)) > 0, print1(eulerphi(k), ", ")));

a(n) = A000010(A032924(n)).

Asymptotic mean of phi(k)/k over A032924: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k)/A032924(k) = 27/(4*Pi^2) = 1/A214549 = 0.683917... (Banks and Shparlinski, 2004).

cp's OEIS Frontend

A371239 Squarefree numbers that are zeroless in base 3 (A032924).

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