A225713 -id:A225713 - cp's OEIS frontend

A225712 Composite squarefree numbers n such that p(i)+2 divides n-2, where p(i) are the prime factors of n.

182, 21827, 32942, 46055, 84502, 151202, 191522, 361802, 532247, 780626, 1368642, 1398377, 1425230, 1556258, 1751927, 1932338, 2209727, 3496502, 4078802, 4216862, 4438709, 5191562, 5991477, 7413002, 8385365, 8797502, 11749127, 13634138, 15921677, 16772177

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 151202 are 2, 19, 23 and 173. We have that (151202-2)/(2+2) = 37800, (151202-2)/(19+2) = 7200, (151202-2)/(23+2) = 6048 and (151202-2)/(173+2)= 864.

Cf. A208728, A225702-A225711, A225713-A225720.

with(numtheory); A225712:=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: A225712(10^9,-2);

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

A225714 Composite squarefree numbers n such that p(i)+4 divides n-4, where p(i) are the prime factors of n.

Original entry on oeis.org

1054, 9541, 91039, 371074, 985054, 1043959, 1063003, 1107754, 1162498, 1357339, 1786054, 4018018, 5368549, 5820154, 8725747, 9994954, 12402709, 17138503, 17914054, 20855839, 23116009, 25077199, 26545054, 29247229, 30308359, 31424419, 33892759, 44141629

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 1043959 are 7, 293 and 509. We have that (1043959-4)/(7+4) = 94905, (1043959-4)/(293+4) = 3515 and (1043959-4)/(509+4) = 2035.

Cf. A208728, A225702-A225713, A225715-A225720.

with(numtheory); A225714:=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: A225714(10^9,-4);

a(20)-a(28) from Donovan Johnson, Nov 15 2013

cp's OEIS Frontend

A225712 Composite squarefree numbers n such that p(i)+2 divides n-2, where p(i) are the prime factors of n.

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