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A274443
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Least composite squarefree number k such that (p-n) | (k-1) for all primes p dividing n.
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4
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561, 21, 85, 15, 21, 35, 33, 21, 65, 91, 57, 91, 133, 55, 161, 91, 57, 133, 33, 253, 65, 91, 145, 115, 217, 451, 161, 703, 253, 551, 561, 253, 481, 217, 129, 451, 301, 1081, 161, 1189, 145, 989, 217, 235, 481, 703, 649, 329, 265, 1081, 1121, 1219, 145, 1037, 721
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OFFSET
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1,1
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LINKS
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EXAMPLE
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Prime factors of 561 are 3, 11 and 17: (561 - 1) / (3 - 1) = 560 / 2 = 280, (561 - 1) / (11 - 1) = 560 / 10 = 56 and (561 - 1) / (17 - 1) = 560 / 16 = 35.
Prime factors of 21 are 3 and 7: (21 - 1) / (3 - 2) = 20 / 1 = 20, (21 - 1) / (7 - 2) = 20 / 5 = 4.
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MAPLE
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with(numtheory); P:=proc(q) local d, k, n, ok, p;
for k from 1 to q do for n from 2 to q do
if not isprime(n) and issqrfree(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][1]=k then ok:=0; break; else
if not type((n-1)/(p[d][1]-k), integer) then ok:=0; break; fi; fi; od;
if ok=1 then print(n); break; fi; fi; od; od; end: P(10^9);
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MATHEMATICA
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t = Select[Range@2000, SquareFreeQ@ # && CompositeQ@ # &]; Table[SelectFirst[t, Function[k, AllTrue[First /@ FactorInteger@ k, If[# == 0, False, Divisible[k - 1, #]] &[# - n] &]]], {n, 55}] (* Michael De Vlieger, Jun 24 2016, Version 10 *)
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CROSSREFS
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Cf. A208728, A225702-A225720, A226020, A226111-A226114, A226364, A226448, A228299-A228302, A229273-A229276, A229321-A229324, A274444, A274445, A274446.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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