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URL: https://oeis.org/A225703

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A225703
Composite squarefree numbers n such that p(i)-3 divides n+3, where p(i) are the prime factors of n.
3
77, 2717, 3245, 18221, 30797, 37177, 46397, 51997, 56573, 61997, 111757, 128573, 149765, 158197, 263117, 264517, 314717, 437437, 475157, 617437, 667573, 683537, 701005, 718333, 834197, 864497, 902957, 904397, 929005, 945277, 1030237, 1096205, 1139653, 1188317
OFFSET
1,1
LINKS
EXAMPLE
Prime factors of 37177 are 7, 47 and 113. We have that (37177+3)/(7-3) = 9295, (37177+3)/(47-3) = 845 and (37177+3)/(113-3) = 338.
MAPLE
with(numtheory); A225703:=proc(i, j) local c, d, n, ok, p, t;
for n from 1 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: A225703(10^9, 3);
MATHEMATICA
t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 3] > 0 && Union[Mod[n + 3, p - 3]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 13 2013
STATUS
approved