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 A093548 a(n) is the smallest number m such that each of the numbers m and m+1 has n distinct prime divisors. 10
 2, 14, 230, 7314, 254540, 11243154, 965009045, 65893166030, 5702759516090, 490005293940084, 76622240600506314 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime factors may be repeated in m and m+1. The difference between this sequence and A052215 is that in the latter, no prime factor may be repeated. So A052215 imposes more stringent conditions, hence a(n) <= A052215(n). - N. J. A. Sloane, Nov 21 2015 2^63 < a(12) <= 22593106657425552170. - Donovan Johnson, Jan 08 2009 A115186(n) <= a(n) <= A052215(n). - Zak Seidov, Jan 16 2015 REFERENCES J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 230, p. 65, Ellipses, Paris 2008. LINKS FORMULA a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ];m) EXAMPLE a(5) = 254540 because 254540=2^2*5*11*13*89; 254541=3*7*17*23*31 and 254540 is the smallest number m which each of the numbers m & m+1 has 5 distinct prime divisors. In contrast, A052215(5) = 378014 > 254540. - N. J. A. Sloane, Nov 21 2015 MATHEMATICA a[n_] := (For[m=1, !(Length[FactorInteger[m]]==n && Length[FactorInteger[m+1]]==n), m++ ]; m); Do[Print[a[n]], {n, 7}] CROSSREFS Cf. A052215 (another version), A093549, A093550, A115186. Sequence in context: A323693 A118086 A048163 * A052215 A053846 A053855 Adjacent sequences:  A093545 A093546 A093547 * A093549 A093550 A093551 KEYWORD nonn,more AUTHOR Farideh Firoozbakht, Apr 06 2004 EXTENSIONS a(8), a(9) from Martin Fuller, Jan 17 2006 a(10)-a(11) from Donovan Johnson, Jan 08 2009 STATUS approved

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Last modified October 21 06:39 EDT 2019. Contains 328292 sequences. (Running on oeis4.)