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A225702 Composite squarefree numbers n such that p-2 divides n+2 for each prime p dividing n. 33
273, 54943, 67303, 199393, 831283, 1097305, 1363723, 1569103, 1590433, 3199579, 3282433, 3503773, 5645563, 5659333, 9260053, 9733843, 9984115, 10738033, 16645363, 19229533, 32168743, 37759363, 38645233, 50806585, 53825497, 56451373, 58327423, 62207173 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
Prime factors of 1097305 are 5, 11, 71 and 281. We have that (1097305+2)/(5-2)= 365769, (1097305+2)/(11-2) = 121923, (1097305+2)/(71-2)= 15903 and (1097305+2)/(281-2) = 3933.
MAPLE
with(numtheory); A225702:=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: A225702(10^9, 2);
MATHEMATICA
t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 2] > 0 && Union[Mod[n + 2, p - 2]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t
PROG
(PARI) is(n, f=factor(n))=if(#f[, 2]<3 || vecmax(f[, 2])>1 || f[1, 1]==2, return(0)); for(i=1, #f~, if((n+2)%(f[i, 1]-2), return(0))); 1 \\ Charles R Greathouse IV, Nov 05 2017
CROSSREFS
Sequence in context: A210270 A351766 A321035 * A307537 A295455 A174771
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 13 2013
EXTENSIONS
Extended by T. D. Noe, May 17 2013
STATUS
approved

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Last modified July 30 22:53 EDT 2024. Contains 374771 sequences. (Running on oeis4.)