A225708 -id:A225708 - cp's OEIS frontend

A225707 Composite squarefree numbers n such that p(i)-7 divides n+7, where p(i) are the prime factors of n.

33, 65, 165, 209, 345, 713, 1353, 2717, 2945, 4433, 4745, 6149, 7733, 9785, 11297, 16985, 21593, 25265, 26273, 28545, 32357, 35673, 47945, 49913, 55913, 61013, 69113, 69513, 88913, 95465, 106913, 116513, 119009, 121785, 133433, 159185, 167765, 201773

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 7733 are 11, 19 and 37. We have that (7733+7)/(11-7) = 1935, (7733+7)/(19-7) = 645 and (7733+7)/(37-7) = 258.

Paolo P. Lava, Table of n, a(n) for n = 1..50

Cf. A208728, A225702-A225706, A225708-A225720.

with(numtheory); A225707:=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: A225707(10^9,7);

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 7] > 0 && Union[Mod[n + 7, p - 7]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

A225709 Composite squarefree numbers n such that p(i)-9 divides n+9, where p(i) are the prime factors of n.

Original entry on oeis.org

15, 21, 33, 35, 39, 55, 77, 91, 119, 143, 195, 231, 255, 299, 455, 551, 651, 663, 715, 935, 1131, 1155, 1419, 2015, 2035, 2431, 3003, 3111, 3927, 4611, 5451, 7215, 7735, 8151, 8671, 9191, 10455, 11571, 15015, 15477, 16511, 18343, 18615, 23541, 24871, 25415, 28391

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 16511 are 11, 19 and 79. We have that (16511+9)/(11-9) = 8260, (16511+9)/(19-9) = 1652 and (16511+9)/(79-9) = 236.

Cf. A208728, A225702-A225708, A225710-A225720.

with(numtheory); A225709:=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: A225709(10^9,9);

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 9, p - 9]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

cp's OEIS Frontend

A225707 Composite squarefree numbers n such that p(i)-7 divides n+7, where p(i) are the prime factors of n.

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