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A225715
Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.
3
165, 1085, 3965, 4085, 5621, 7733, 8645, 14405, 19877, 23405, 33269, 40397, 45365, 66929, 88949, 110885, 114917, 135005, 243941, 275621, 280085, 421085, 439565, 455285, 460229, 474677, 480245, 496589, 505517, 518081, 570245, 706805, 709973, 900581, 912021
OFFSET
1,1
LINKS
EXAMPLE
Prime factors of 7733 are 11, 19 and 37. We have that (7733-5)/(11+5) = 483, (7733-5)/(19+5) = 322 and (7733-5)/(37+5) = 184.
MAPLE
with(numtheory); A225715:=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: A225715(10^9, -5);
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 - 5, p + 5]] == {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