A248502 Numbers m that are not coprime to floor(m/16).

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 32, 34, 36, 38, 40, 42, 44, 46, 48, 51, 54, 57, 60, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 85, 90, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 119, 126, 128, 130, 132, 134, 136, 138, 140, 142

Offset

1,1

Comments

Definition of 'being coprime' and special-case conventions are as in Wikipedia. In particular, when m < 16 then floor(m/16) = 0, and zero is coprime only to 1. The complementary sequence is A248501.

The asymptotic density of this sequence is 1 - A250031(16)/A250033(16) = 199663/480480 = 0.415549... . - Amiram Eldar, Nov 30 2024

Links

Stanislav Sykora, Table of n, a(n) for n = 1..20000

Wikipedia, Coprime integers.

Formula

gcd(a(n),floor(a(n)/16)) > 1.

Example

2 is a term because gcd(2,0) = 2 > 1.
21 is not a term because floor(21/16) = 1 and 1 is coprime to any number.
200 is a term because floor(200/16) = 12 and gcd(200,12) = 4 > 1.

Mathematica

Select[Range[150], !CoprimeQ[#, Floor[#/16]] &] (* Amiram Eldar, Nov 30 2024 *)

Prog

(PARI) a=vector(20000);
i=n=0; while(i++, if(gcd(i, i\16)!=1, a[n++]=i; if(n==#a, break))); a

Crossrefs

Cf. A248499, A248500, A248501, A250031, A250033.

Sequence in context: A032950 A365684 A309127 * A250039 A132032 A341709

Adjacent sequences: A248499 A248500 A248501 * A248503 A248504 A248505

Keyword

nonn,base,easy

Author

Stanislav Sykora, Oct 07 2014

Status

approved