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A225717
Composite squarefree numbers n such that p(i)+7 divides n-7, where p(i) are the prime factors of n.
3
1015, 4147, 7567, 9367, 13447, 15847, 25543, 29127, 33847, 39319, 40807, 58327, 80647, 87607, 116071, 135439, 139867, 145915, 177415, 186667, 190747, 203287, 222343, 253897, 321127, 356167, 380887, 384391, 391207, 403495, 453607, 470587, 501607, 602167, 606535
OFFSET
1,1
LINKS
EXAMPLE
Prime factors of 15847 are 13, 23 and 53. We have that (15847-7)/(13+7) = 792, (15847-7)/(23+7) = 528 and (15847-7)/(53+7) = 264.
MAPLE
with(numtheory); A225717:=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: A225717(10^9, -7);
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 - 7, p + 7]] == {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