A225715 -id:A225715 - cp's OEIS frontend

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

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

A225716 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, 26781, 120791, 5099531, 5720435, 14637451, 24110358, 31552261, 33792198, 57804181, 71925054, 88324781, 92849126, 441031331, 650715071, 924029951, 1425902869, 2093676486, 2336689491, 3273172441, 4533042611, 4711366831, 5162021871, 5502040431, 6427899582

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 14637451 are 41, 229 and 1559. We have that (14637451-6)/(41+6) = 311435, (14637451-6)/(229+6) = 62287 and (14637451-6)/(1559+6) = 9353.

Cf. A208728, A225702-A225715, A225717-A225720.

with(numtheory); A225716:=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: A225716(10^9,-6);

a(14)-a(25) from Donovan Johnson, Nov 15 2013

cp's OEIS Frontend

A225714 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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