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t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 3, p + 3]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

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Composite squarefree numbers n such that p(i)+3| divides n-3, where p(i) are the prime factors of n.

Prime factors of 5883 are 3, 37 and 53. We have that (3+3)|/(5883-3) = 980, (37+3)|/(5883-3) = 147 and (53+3)|/(5883-3) = 105.

Cf. A208728, A225702-A225712, A225714-A225720.

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Paolo P. Lava, <a href="/A225713/b225713.txt">Table of n, a(n) for n = 1..100</a>

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: A225713(10^9, -3);

allocated for Paolo P. Lava

Composite squarefree numbers n such that p(i)+3|n-3, where p(i) are the prime factors of n.

195, 1235, 1443, 2915, 4403, 5883, 35203, 37635, 54723, 66563, 77503, 97555, 157403, 158403, 188355, 200203, 265411, 273003, 299715, 317203, 358179, 376995, 380373, 438243, 476003, 492803, 506883, 511683, 567633, 630203, 636803, 654951, 742269, 764463, 827203

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Prime factors of 5883 are 3, 37 and 53. We have that (3+3)|(5883-3)=980, (37+3)|(5883-3)=147 and (53+3)|(5883-3)=105.

with(numtheory); A225713:=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: A225713(10^9, -3);

Cf. A208728, A225702-A225712, A225714-A225720

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Paolo P. Lava, May 13 2013

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allocated for Paolo P. Lava

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