A227973 -id:A227973 - cp's OEIS frontend

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

Paolo P. Lava, Aug 06 2013

nonn

			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.

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

Cf. A208728, A225702-A225720, A227973-A227974.

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

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.

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