A227976 -id:A227976 - cp's OEIS frontend

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

Paolo P. Lava, Aug 02 2013

nonn

			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.

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

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

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);

A227974 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 .

Original entry on oeis.org

385, 182, 195, 1054, 165, 6, 1015, 4958, 2193, 10, 5159, 113937, 5593, 14, 15, 196009, 3657, 6318638, 2755, 1227818, 21, 22, 2795, 152358, 12121, 26, 21827, 17578, 36569, 30, 38335, 457907, 33, 34, 35

Offset: 1

Paolo P. Lava, Aug 02 2013

nonn

Fixed points are the squarefree semiprimes.

			For n=3 the minimum k is 195. Prime factors of 195 are 3, 5 and 13. We have: 195 - 3 = 192, 3 + 3 = 6 and 192 / 6 = 32, 5 + 3 = 8 and 192 / 8 = 24, 13 + 3 = 16 and 192 / 16 = 12.

Cf. A208728, A225702-A225720, A227973, A227976.

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 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);

cp's OEIS Frontend

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.

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