A225707 -id:A225707 - cp's OEIS frontend

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

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

A225708 Composite squarefree numbers n such that p(i)-8 divides n+8, where p(i) are the prime factors of n.

Original entry on oeis.org

10, 22, 55, 70, 154, 190, 322, 385, 442, 595, 682, 2002, 2737, 3619, 5530, 14986, 23782, 24817, 25102, 26767, 30430, 31042, 34762, 37810, 85462, 106582, 141427, 171790, 189727, 225910, 243217, 248482, 255142, 272782, 307090, 381547, 388102, 471262, 637849, 798490

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 381547 are 23, 53 and 313. We have that (381547+8)/(23-8)=25437, (381547+8)/(53-8)=8479 and (381547+8)/(313-8)=1251.

Cf. A208728, A225702-A225707, A225709-A225720.

with(numtheory); A225708:=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: A225708(10^9,8);

t = {}; n = 0; While[Length[t] < 40, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n + 8, p - 8]] == {0}, AppendTo[t, n]]]; t (* T. D. Noe, May 17 2013 *)

cp's OEIS Frontend

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

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