A225716 -id:A225716 - cp's OEIS frontend

A225715 Composite squarefree numbers n such that p(i)+5 divides n-5, where p(i) are the prime factors of n.

165, 1085, 3965, 4085, 5621, 7733, 8645, 14405, 19877, 23405, 33269, 40397, 45365, 66929, 88949, 110885, 114917, 135005, 243941, 275621, 280085, 421085, 439565, 455285, 460229, 474677, 480245, 496589, 505517, 518081, 570245, 706805, 709973, 900581, 912021

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 7733 are 11, 19 and 37. We have that (7733-5)/(11+5) = 483, (7733-5)/(19+5) = 322 and (7733-5)/(37+5) = 184.

Paolo P. Lava, Table of n, a(n) for n = 1..150

Cf. A208728, A225702-A225714, A225716-A225720.

with(numtheory); A225715:=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: A225715(10^9,-5);

t = {}; n = 0; len = -2; While[len <= 262, n++; {p, e} = Transpose[FactorInteger[n]]; If[Length[p] > 1 && Union[e] == {1} && Union[Mod[n - 5, p + 5]] == {0}, AppendTo[t, n]; len = len + Length[IntegerDigits[n]] + 2]]; t (* T. D. Noe, May 17 2013 *)

A225717 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

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 *)

cp's OEIS Frontend

A225715 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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