A225715 -id:A225715

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A225714

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

+10
3

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

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.

MAPLE

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);

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 13 2013

EXTENSIONS

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

STATUS

approved

A225716

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

+10
3

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