cp's OEIS Frontend

A382484 Least composite squarefree numbers k > n such that p + n divides k - n, for each prime p dividing k.

%I A382484 #18 Mar 30 2025 09:49:12
%S A382484 385,182,195,1054,165,26781,1015,4958,2193,79222,5159,113937,5593,
%T A382484 160937,6351,196009,3657,6318638,2755,1227818,12669,41302,2795,152358,
%U A382484 12121,366821,21827,17578,36569,12677695,38335,457907,2553,15334,141155,69722351,1045,14003,4823,2943805
%N A382484 Least composite squarefree numbers k > n such that p + n divides k - n, for each prime p dividing k.
%e A382484 a(20) = 1227818 = 2 * 19 * 79 * 409 and
%e A382484   (1227818 - 20) /(2 + 20) = 55809;
%e A382484   (1227818 - 20) /(19 + 20) = 31482;
%e A382484   (1227818 - 20) /(79 + 20) = 12402;
%e A382484   (1227818 - 20) /(409 + 20) = 2862.
%p A382484 with(numtheory): P:=proc(q) local d,k,ok,n,p;
%p A382484 for n from 1 to 17 do for k from n+1 to q do
%p A382484 if issqrfree(k) and not isprime(k) then p:=factorset(k); ok:=1;
%p A382484 for d from 1 to nops(p) do if frac((k-n)/(p[d]+n))>0 then ok:=0;
%p A382484 break; fi; od; if ok=1 then lprint(n,k); break; fi; fi; od; od; end: P(10^8);
%o A382484 (PARI) isok(k,n) = if (!issquarefree(k) || isprime(k), return(0)); my(f=factor(k)[,1]); for (i=1, #f, if ((k-n) % (f[i]+n), return(0));); return(1);
%o A382484 a(n) = my(k=n+1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, Mar 30 2025
%Y A382484 Cf. A208728, A225702-A225710, A225711-A225720.
%K A382484 nonn
%O A382484 1,1
%A A382484 _Paolo P. Lava_, Mar 29 2025
%E A382484 More terms from _Michel Marcus_, Mar 30 2025