A274445 a(n) is the smallest composite squarefree number k such that (p+n) | (k-1) for every prime p dividing k.

385, 91, 65, 451, 33, 170171, 145, 1261, 161, 78409, 469, 294061, 649, 13051, 1921, 5251, 721, 8453501, 145, 300243, 1121, 47611, 3601, 1915801, 1057, 41311, 545, 5671, 1261, 19723133, 4321, 37759, 6913, 451, 4033, 102821, 1513, 40891, 11521, 1259497, 721, 364781, 145

Offset

1,1

Links

Jinyuan Wang, Table of n, a(n) for n = 1..100

Example

For n=1, prime factors of 385 are 5, 7 and 11. (385 - 1)/(5 + 1) = 384/6 = 64, (385 - 1)/(7 + 1) = 384/8 = 48 and (385 - 1)/(11 + 1) = 384/12 = 32.
For n=2, prime factors of 91 are 7 and 13. (91 - 1)/(7 + 2) = 90/9 = 10 and (91 - 1)/(13 + 2) = 90/15 = 6.

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[10^6], SquareFreeQ@ # && CompositeQ@ # &]; Table[ SelectFirst[t, Function[k, AllTrue[First /@ FactorInteger@ k, Divisible[k - 1, # + n] &]]], {n, 17}] (* 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, A274446.

Sequence in context: A067518 A071763 A254352 * A227974 A069043 A013591

Adjacent sequences: A274442 A274443 A274444 * A274446 A274447 A274448

Keyword

nonn

Author

Paolo P. Lava, Jun 23 2016

Extensions

a(18), a(24), a(30) added by Giovanni Resta, Jun 23 2016

More terms from Michel Marcus, Jun 28 2016

Status

approved