A160811 Numbers not dividing 24.

5, 7, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset: 1

Author

Omar E. Pol, Jun 19 2009, Jun 28 2009

Keywords

• easy
• nonn

Comments

These terms m > 5 can be called "triphile" or "3-phile" numbers, because there are 3 positive integers b_1 < b_2 < b_3 such that b_1 divides b_2, b_2 divides b_3 and m = b_1 + b_2 + b_3. A number that is not "triphile" is called "triphobe" or "3-phobe" (A019532). The smallest triphile number is 7 = 1 + 2 + 4 and the largest triphobe is 24. See A348517 for more explanations and link. - Bernard Schott, Oct 21 2021

Links

• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos
• Omar E. Pol, Divisors and pi(x)
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Complement of A018253.

Cf. A000005, A000720, A161205.

Cf. A019532, A348517.

Programs

Mathematica

Complement[Range[100],Divisors[24]] (* Harvey P. Dale, May 13 2019 *)

PARI

is(n)=!!n%24 \\ Charles R Greathouse IV, Oct 26 2011

Formula

a(n) = n + 8 for n > 16. [Charles R Greathouse IV, Oct 26 2011]

Extensions

Definition corrected by Omar E. Pol, Nov 17 2009