This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A226364 #13 Jun 07 2013 13:17:07 %S A226364 308267,1420467,1445995,46874667,153810067,324218667,355724747, %T A226364 393253747,471957547,618729307,886489707,901990059,1062803467, %U A226364 1525582667,1735517355,4306362667,4815895467,6528285867,6634856107,11460166667,12364885867,13330858667,20628538667 %N A226364 Composite squarefree numbers n such that the ratios (n - 1/3)/(p - 1/3) are integers for each prime p dividing n. %C A226364 Also composite squarefree numbers n such that (3p - 1) | (3n - 1). %H A226364 Giovanni Resta, <a href="/A226364/b226364.txt">Table of n, a(n) for n = 1..68</a> (terms < 2*10^12) %e A226364 The prime factors of 1445995 are 5, 19, 31 and 491. We see that (1445995 - 1/3)/(5 - 1/3) = 309856, (1445995 - 1/3)/(19 - 1/3) = 77464, (1445995 - 1/3)/(31 - 1/3) = 47152 and (1445995 - 1/3)/(491 - 1/3) = 2947. Hence 1445995 is in the sequence. %e A226364 The prime factors of 1112307 are 3, 7 and 52967. We see that (1112307 - 1/3)/(3 - 1/3) = 417115, (1112307 - 1/3)/(7 - 1/3) = 166846 but (1112307 - 1/3)/(52967 - 1/3) = 166846/7945. Hence 1112307 is not in the sequence. %p A226364 with(numtheory); ListA226364:=proc(i, j) local c, d, n, ok, p; %p A226364 for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1; %p A226364 for d from 1 to nops(p) do if p[d][2]>1 or not type((n-j)/(p[d][1]-j),integer) then ok:=0; break; fi; od; %p A226364 if ok=1 then print(n); fi; fi; od; end: ListA226364(10^9,1/3); %o A226364 (PARI) is(n,P)=n=3*n-1; for(i=1,#P,if(n%(3*P[i]-1),return(0))); 1 %o A226364 list(lim,P=[],n=1,mx=lim\2)=my(v=[],t);if(#P>1&&is(n,P), v=[n]); P=concat(P,0); forprime(p=2,min(lim,mx),P[#P]=p;t=list(lim\p,P,n*p,p-1);if(#t,v=concat(v,t))); v \\ _Charles R Greathouse IV_, Jun 07 2013 %Y A226364 Cf. A208728, A225702-A225720, A226020, A226111-A226114, A226448. %K A226364 nonn %O A226364 1,1 %A A226364 _Paolo P. Lava_, Jun 05 2013 %E A226364 a(5)-a(23) from _Giovanni Resta_, Jun 07 2013