A121058 Positive integers x such that x+d+1 is composite for all divisors d of x.

7, 13, 19, 22, 31, 37, 42, 43, 46, 47, 49, 61, 62, 67, 73, 79, 82, 91, 97, 103, 109, 118, 121, 122, 126, 127, 133, 139, 142, 151, 157, 163, 166, 167, 169, 172, 181, 193, 199, 202, 206, 211, 212, 213, 214, 217, 218, 223, 229, 241, 242, 246, 247, 250, 256, 257

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Walter A. Kehowski, D Numbers.

Formula

a(n)=n-th number x such that x+d+1 is composite for all divisors d of x.

Example

a(9)=46=2*23 since 46+1+1=48=16*3, 46+2+1=49=7*7, 46+23+1=70=2*5*7, 46+46+1=93=3*31.

Maple

with(numtheory): cnt:=0: L:=[]: for w to 1 do for n from 1 while cnt<100 do dn:=divisors(n); Q:=map(z-> n+z+1, dn); if andmap(z-> not isprime(z), Q) then cnt:=cnt+1; L:=[op(L), [cnt, n]]; fi; od od; L;

Mathematica

Select[Range[300], AllTrue[#+1+Divisors[#], CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 05 2015 *)

Crossrefs

Cf. A120806.

Sequence in context: A232436 A274437 A031194 * A007921 A092409 A124095

Adjacent sequences: A121055 A121056 A121057 * A121059 A121060 A121061

Keyword

nonn

Author

Walter Kehowski, Aug 09 2006

Status

approved