A225706 -id:A225706 - cp's OEIS frontend

A225705 Composite squarefree numbers n such that p(i)-5 divides n+5, where p(i) are the prime factors of n.

21, 91, 187, 391, 3451, 4147, 6391, 7579, 8827, 9499, 9823, 11803, 15283, 21307, 22243, 26887, 29563, 36091, 42763, 49387, 62491, 63427, 84091, 89947, 107707, 116083, 126451, 139867, 155227, 227263, 270391, 287419, 302731, 317191, 320827, 376987, 381667, 433939

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 6391 are 7, 11 and 83. We have that (6391+5)/(7-5)  =3198, (6391+5)/(11-5) = 1066 and (6391+5)/(83-5) = 82.

Paolo P. Lava, Table of n, a(n) for n = 1..100

Cf. A208728, A225702-A225704, A225706-A225720.

with(numtheory); A225705:=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: A225705(10^9,5);

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Mod[n, 5] > 0 && Union[Mod[n + 5, p - 5]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

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

Original entry on oeis.org

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 *)

cp's OEIS Frontend

A225705 Composite squarefree numbers n such that p(i)-5 divides n+5, where p(i) are the prime factors of n.

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