A227976 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.

561, 1595, 35, 6, 21, 6, 15, 14, 21, 10, 35, 22, 33, 14, 15, 133, 65, 34, 51, 38, 21, 22, 95, 46, 69, 26, 115, 217, 161, 30, 87, 62, 33, 34, 35, 1247, 217, 38, 39, 817, 185, 42, 123, 86, 129, 46, 215, 94, 141, 1247, 51, 1802, 329, 106, 55, 1541, 57, 58, 371

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..200

Example

For n=2 the minimum k is 1595. Prime factors of 1595 are 5, 11, and 29. We have 1595 - 2 = 1593, 5 - 2 = 2 and 1593 / 3 = 531, 11 - 2 = 9 and 1593 / 9 = 177, 29 - 2 = 27 and 1593 / 27 = 59.

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, A227973-A227974.

Sequence in context: A309268 A131672 A321156 * A224930 A083732 A292367

Adjacent sequences: A227973 A227974 A227975 * A227977 A227978 A227979

Keyword

nonn

Author

Paolo P. Lava, Aug 06 2013

Status

approved