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Let d(n) = number of distinct primes dividing n (A001221). Find smallest t such that d(t)=d(t+1)=...=d(t+n-1) but d(t-1) and d(t+n) are not = d(t); then a(n)=t.
6

%I #11 Oct 13 2012 15:19:43

%S 1,14,7,2,54,91,323,141,44360,48919,218972,534078,2699915,526095,

%T 17233173,127890362,29138958036,146216247221,118968284928

%N Let d(n) = number of distinct primes dividing n (A001221). Find smallest t such that d(t)=d(t+1)=...=d(t+n-1) but d(t-1) and d(t+n) are not = d(t); then a(n)=t.

%C a(n) > 10^13 for n from 20 to 22. a(23) = 585927201062. [From _Donovan Johnson_, Jul 30 2010]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicNumber.html">Cubic number.</a>

%e a(3)=7 since 7,8,9 all have d = 1 but d(6) and d(10) != 1 and this is the first run of 3.

%Y First occurrence of a run of length exactly n in A001221. Cf. A048971, A048972.

%K easy,nonn

%O 1,2

%A _Enoch Haga_

%E More terms from _Naohiro Nomoto_, Jul 13 2001

%E a(16)-a(19) from _Donovan Johnson_, Jul 30 2010