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%I #13 Aug 09 2020 17:07:10
%S 7,13,19,22,31,37,42,43,46,47,49,61,62,67,73,79,82,91,97,103,109,118,
%T 121,122,126,127,133,139,142,151,157,163,166,167,169,172,181,193,199,
%U 202,206,211,212,213,214,217,218,223,229,241,242,246,247,250,256,257
%N Positive integers x such that x+d+1 is composite for all divisors d of x.
%H Harvey P. Dale, <a href="/A121058/b121058.txt">Table of n, a(n) for n = 1..1000</a>
%H Walter A. Kehowski, <a href="http://web.gccaz.edu/~walof42631/propertyd/index.html">D Numbers</a>.
%F a(n)=n-th number x such that x+d+1 is composite for all divisors d of x.
%e 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.
%p 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;
%t Select[Range[300],AllTrue[#+1+Divisors[#],CompositeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 05 2015 *)
%Y Cf. A120806.
%K nonn
%O 1,1
%A _Walter Kehowski_, Aug 09 2006
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