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.

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

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