A225718 -id:A225718 - cp's OEIS frontend

A225717 Composite squarefree numbers n such that p(i)+7 divides n-7, where p(i) are the prime factors of n.

1015, 4147, 7567, 9367, 13447, 15847, 25543, 29127, 33847, 39319, 40807, 58327, 80647, 87607, 116071, 135439, 139867, 145915, 177415, 186667, 190747, 203287, 222343, 253897, 321127, 356167, 380887, 384391, 391207, 403495, 453607, 470587, 501607, 602167, 606535

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 15847 are 13, 23 and 53. We have that (15847-7)/(13+7) = 792, (15847-7)/(23+7) = 528 and (15847-7)/(53+7) = 264.

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

Cf. A208728, A225702-A225716, A225718-A225720.

with(numtheory); A225717:=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: A225717(10^9,-7);

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 7, p + 7]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

A225719 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

2193, 3705, 9889, 12749, 23529, 116265, 283929, 514569, 641769, 661789, 772809, 950609, 1144313, 1241561, 1452009, 1708233, 1797609, 1878569, 2244901, 2255689, 2675409, 2792937, 3426089, 4021369, 4187465, 5242569, 7327329, 7942209, 8601329, 8668921, 9608729

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 116265 are 3, 5, 23 and 337. We have that (116265-9)/(3+9) = 9688, (116265-9)/(5+9) = 8304, (116265-9)/(23+9) = 3633 and (116265-9)/(337+9) = 336.

Cf. A208728, A225702-A225718, A225720.

with(numtheory); A225719:=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: A225719(10^9,-9);

cp's OEIS Frontend

A225717 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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