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A227973 Minimum composite squarefree numbers k such that p(i)-n divides k+n, for n=1, 2, 3, 4,..., where p(i) are the prime factors of k. 3
15, 273, 77, 6, 21, 6, 33, 10, 15, 14, 21, 33, 35, 22, 33, 26, 39, 57, 65, 34, 51, 38, 57, 551, 95, 46, 69, 203, 115, 145, 161, 58, 87, 62, 93, 629, 155, 697, 217, 74, 111, 518, 185, 82, 123, 86, 129, 2537, 215, 94, 141, 689, 235, 4366, 329, 106, 159, 1247, 265 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..500

EXAMPLE

For n=185 the minimum k is 543. Prime factors of 543 are 3 and 181. We have: 543 + 185 = 728, 3 - 185 = -182 and 728 / (-182) = -4, 181 - 185 = -4 and 728 / (-4) = 182.

MAPLE

with(numtheory); P:=proc(i) local c, d, k, n, ok, p; for k from 1 to i do

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]=k then ok:=0; break; fi;

if  not type((n+k)/(p[d][1]-k), integer) then ok:=0; break; fi; od;

if ok=1 then print(n); break; fi; fi; od; od; end: P(10^6);

CROSSREFS

Cf. A208728, A225702-A225720, A227974-A227976.

Sequence in context: A013384 A013380 A013382 * A195615 A156091 A194728

Adjacent sequences:  A227970 A227971 A227972 * A227974 A227975 A227976

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Aug 02 2013

STATUS

approved

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Last modified June 26 23:17 EDT 2022. Contains 354885 sequences. (Running on oeis4.)