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Smallest k such that (10^k - 1)/9 has n distinct prime divisors. Or a(n)= smallest value of k such that A000042(k) has exactly n distinct prime divisors.
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%I #18 Apr 29 2022 23:31:23

%S 1,2,3,9,8,6,15,12,18,45,24,32,54,30,42,64,102,72,108,154,60,84,96,

%T 140,126,200,120,204,308,168,192,280,180,210,240,252,330

%N Smallest k such that (10^k - 1)/9 has n distinct prime divisors. Or a(n)= smallest value of k such that A000042(k) has exactly n distinct prime divisors.

%C a(40) = 300; all other subsequent terms are > 322. - _Ray Chandler_, Apr 23 2017

%C a(38) = 336. - _Max Alekseyev_, Apr 29 2022

%o (PARI) a(n) = my(k=1); while(omega((10^k - 1)/9) !=n, k++); k; \\ _Michel Marcus_, Apr 23 2017

%Y Cf. A000042, A001221, A002275, A095370.

%K more,nonn

%O 0,2

%A _Amarnath Murthy_, Aug 31 2003

%E Corrected and extended by _Sascha Kurz_, Sep 22 2003

%E a(12)-a(15) from _David Wasserman_, Mar 28 2005

%E a(16)-a(27) from _Donovan Johnson_, Nov 17 2008

%E a(28)-a(35) from _Ray Chandler_, Apr 23 2017

%E a(36) from _Max Alekseyev_, Apr 29 2022