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

385, 182, 195, 1054, 165, 26781, 1015, 4958, 2193, 79222, 5159, 113937, 5593, 160937, 6351, 196009, 3657, 6318638, 2755, 1227818, 12669, 41302, 2795, 152358, 12121, 366821, 21827, 17578, 36569, 12677695, 38335, 457907, 2553, 15334, 141155, 69722351, 1045, 14003, 4823, 2943805

Offset: 1

Author

Paolo P. Lava, Mar 29 2025

Keywords

• nonn

Examples

			a(20) = 1227818 = 2 * 19 * 79 * 409 and
  (1227818 - 20) /(2 + 20) = 55809;
  (1227818 - 20) /(19 + 20) = 31482;
  (1227818 - 20) /(79 + 20) = 12402;
  (1227818 - 20) /(409 + 20) = 2862.
		

Crossrefs

Cf. A208728, A225702-A225710, A225711-A225720.

Programs

Maple

with(numtheory): P:=proc(q) local d,k,ok,n,p;
for n from 1 to 17 do for k from n+1 to q do
if issqrfree(k) and not isprime(k) then p:=factorset(k); ok:=1;
for d from 1 to nops(p) do if frac((k-n)/(p[d]+n))>0 then ok:=0;
break; fi; od; if ok=1 then lprint(n,k); break; fi; fi; od; od; end: P(10^8);

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);
a(n) = my(k=n+1); while (!isok(k, n), k++); k; \\ Michel Marcus, Mar 30 2025

Extensions

More terms from Michel Marcus, Mar 30 2025