A225711 Composite squarefree numbers n such that p(i)+1 divides n-1, where p(i) are the prime factors of n.

385, 2737, 6061, 6721, 17641, 24769, 25201, 31521, 34561, 49105, 66385, 76609, 79401, 113221, 136081, 180481, 194833, 199801, 254881, 268801, 311905, 321937, 328321, 362881, 436645, 469201, 506521, 545905, 547561, 558145, 628705, 642505, 649153, 778261, 884305

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..150

Qi-Yang Zheng, There are infinitely many (-1,1)-Carmichael numbers, arXiv:2207.08641 [math.NT], 2022.

Example

Prime factors of 24769 are 17, 31 and 47. We have that (24769-1)/(17+1) = 1376, (24769-1)/(31+1) = 774 and (24769-1)/(47+1) = 516.

Maple

with(numtheory); A225711:=proc(i, j) local c, d, n, ok, p, t;
for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
if  not type((n+j)/(p[d][1]-j), integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: A225711(10^9, -1);

Mathematica

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 1, p + 1]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

Crossrefs

Cf. A208728, A225702-A225710, A225712-A225720.

Sequence in context: A157354 A372319 A200525 * A351696 A204712 A237102

Adjacent sequences: A225708 A225709 A225710 * A225712 A225713 A225714

Keyword

nonn

Author

Paolo P. Lava, May 13 2013

Status

approved