A225705 -id:A225705 - cp's OEIS frontend

A225704 Composite squarefree numbers n such that p(i)-4 divides n+4, where p(i) are the prime factors of n.

6, 10, 14, 15, 30, 35, 66, 266, 455, 806, 4154, 4686, 6665, 10370, 16646, 22781, 31146, 36305, 72086, 205871, 246506, 473711, 570011, 653666, 733586, 900581, 904046, 1422410, 1941971, 1969565, 2023010, 2807255, 2821269, 3009821, 3043274, 3355271, 3880301

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 205871 are 29, 31 and 229. We have that (205871+4)/(29-4) = 8235, (205871+4)/(31-4) = 7625 and (205871+4)/(229-4) = 915.

Cf. A208728, A225702, A225703, A225705-A225720.

with(numtheory); A225704:=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: A225704(10^9,4);

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 4, p - 4]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

Extended by T. D. Noe, May 17 2013

A225706 Composite squarefree numbers n such that p(i)-6 divides n+6, where p(i) are the prime factors of n.

Original entry on oeis.org

6, 10, 14, 15, 21, 30, 35, 42, 70, 78, 105, 154, 170, 210, 357, 759, 1110, 6195, 42465, 43554, 61755, 94605, 106386, 146910, 189399, 229119, 276914, 453590, 924099, 1239870, 2407119, 3915714, 4404394, 4524074, 5819145, 7396394, 8324869, 23701854, 30242654, 33413919

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 8324869 are 7, 19, 53 and 1181. We have that (8324869+6)/(7-6) = 8324875, (8324869+6)/(19-6) = 640375, (8324869+6)/(53-6) = 177125 and (8324869+6)/(1181-6) = 7085.

Cf. A208728, A225702-A225705, A225707-A225720.

with(numtheory); A225706:=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: A225706(10^9,6);

t = {}; n = 0; While[Length[t] < 50, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 6, p - 6]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

Extended by T. D. Noe, May 17 2013

cp's OEIS Frontend

A225704 Composite squarefree numbers n such that p(i)-4 divides n+4, where p(i) are the prime factors of n.

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