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 A274445 a(n) is the smallest composite squarefree number k such that (p+n) | (k-1) for every prime p dividing k. 3
 385, 91, 65, 451, 33, 170171, 145, 1261, 161, 78409, 469, 294061, 649, 13051, 1921, 5251, 721, 8453501, 145, 300243, 1121, 47611, 3601, 1915801, 1057, 41311, 545, 5671, 1261, 19723133, 4321, 37759, 6913, 451, 4033, 102821, 1513, 40891, 11521, 1259497, 721, 364781, 145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE For n=1, prime factors of 385 are 5, 7 and 11. (385 - 1)/(5 + 1) = 384/6 = 64, (385 - 1)/(7 + 1) = 384/8 = 48 and (385 - 1)/(11 + 1) = 384/12 = 32. For n=2, prime factors of 91 are 7 and 13. (91 - 1)/(7 + 2) = 90/9 = 10 and (91 - 1)/(13 + 2) = 90/15 = 6. MAPLE 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 not type((n-1)/(p[d][1]+k), integer) then ok:=0; break; fi; od; if ok=1 then print(n); break; fi; fi; od; od; end: P(10^9); MATHEMATICA t = Select[Range[10^6], SquareFreeQ@ # && CompositeQ@ # &]; Table[ SelectFirst[t, Function[k, AllTrue[First /@ FactorInteger@ k, Divisible[k - 1, # + n] &]]], {n, 17}] (* Michael De Vlieger, Jun 24 2016, Version 10 *) PROG (PARI) isok(k, n)=if (! issquarefree(k), return (0)); vp = factor(k) [, 1]; if (#vp == 1, return (0)); for (i=1, #vp, if ((k-1) % (n+vp[i]), return (0)); ); 1; a(n) = my(k=2); while (! isok(k, n), k++); k; \\ Michel Marcus, Jun 28 2016 CROSSREFS Cf. A208728, A225702-A225720, A226020, A226111-A226114, A226364, A226448, A228299-A228302, A229273-A229276, A229321-A229324, A274443, A274444, A274446. Sequence in context: A067518 A071763 A254352 * A227974 A069043 A013591 Adjacent sequences:  A274442 A274443 A274444 * A274446 A274447 A274448 KEYWORD nonn,more AUTHOR Paolo P. Lava, Jun 23 2016 EXTENSIONS a(18), a(24), a(30) added by Giovanni Resta, Jun 23 2016 More terms from Michel Marcus, Jun 28 2016 STATUS approved

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Last modified June 6 10:55 EDT 2020. Contains 334840 sequences. (Running on oeis4.)