A274446 a(n) is the smallest composite squarefree number k such that (p+n) | (k+1) for all primes dividing k.

399, 299, 55, 611, 143, 5549, 39, 155, 493, 615383, 713, 3247, 119, 1304489, 1333, 31415, 2599, 749, 2183, 440153, 155, 75499, 119, 168600949, 4223, 223649, 559, 66299, 6407, 15157, 3431, 85499, 799, 31589, 7313

Offset

1,1

Links

Table of n, a(n) for n=1..35.

Example

Prime factors of 399 are 3, 7 and 19. (399 + 1) / (3 + 1) = 400 / 4 = 100, (399 + 1) / (7 + 1) = 400 / 8 = 50 and (399 + 1) / (19 + 1) = 400 / 20 = 20.
Prime factors of 299 are 13 and 23. (399 + 1) / (13 + 2) = 300 / 15 = 20 and (399 + 1) / (23 + 2) = 300 / 25 = 12.

Maple

with(numtheory); P:=proc(q) local d, k, n, ok, p;
for k from 1 to q do for n from 2 to q do
if not isprime(n) and issqrfree(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do
if not type((n+1)/(p[d][1]+k), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); break; fi; fi; od; od; end: P(10^9);

Mathematica

t = Select[Range[2000000], SquareFreeQ@ # && CompositeQ@ # &]; Table[SelectFirst[t, Function[k, AllTrue[First /@ FactorInteger@ k, Divisible[k + 1, # + n] &]]], {n, 23}] (* Michael De Vlieger, Jun 24 2016, Version 10 *)

Prog

(PARI) isok(k, n) = {if (! issquarefree(k), return (0)); vp = factor(k) [, 1]; if (#vp == 1, return (0)); for (i=1, #vp, if ((k+1) % (n+vp[i]), return (0)); ); 1; }
a(n) = {my(k=2); while (! isok(k, n), k++); k; } \\ Michel Marcus, Jun 28 2016

Crossrefs

Cf. A208728, A225702-A225720, A226020, A226111-A226114, A226364, A226448, A228299-A228302, A229273-A229276, A229321-A229324, A274443, A274444, A274445.

Sequence in context: A187515 A235569 A261768 * A253598 A046013 A352360

Adjacent sequences: A274443 A274444 A274445 * A274447 A274448 A274449

Keyword

nonn,easy

Author

Paolo P. Lava, Jun 23 2016

Extensions

a(24) from Giovanni Resta, Jun 23 2016

Status

approved