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A048932 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.

%I A048932 #30 Jun 22 2025 16:29:18
%S A048932 1,14,7,2,54,91,323,141,44360,48919,218972,534078,2699915,526095,
%T A048932 17233173,127890362,29138958036,146216247221,118968284928,
%U A048932 2500769994070,3157129230489,22498525938216,585927201062,313978488186061,571560399902283,453918847597184
%N A048932 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 A048932 a(n) > 10^13 for n from 20 to 22. a(23) = 585927201062. - _Donovan Johnson_, Jul 30 2010
%C A048932 a(28) > 2 * 10^15. - _Toshitaka Suzuki_, Jun 22 2025
%H A048932 Toshitaka Suzuki, <a href="/A048932/b048932.txt">Table of n, a(n) for n = 1..27</a>
%H A048932 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubicNumber.html">Cubic number</a>.
%e A048932 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 A048932 First occurrence of a run of length exactly n in A001221. Cf. A048971, A048972.
%K A048932 nonn
%O A048932 1,2
%A A048932 _Enoch Haga_
%E A048932 More terms from _Naohiro Nomoto_, Jul 13 2001
%E A048932 a(16)-a(19) and a(23) from _Donovan Johnson_, Jul 30 2010
%E A048932 a(20)-a(22) from _Toshitaka Suzuki_, Mar 24 2025
%E A048932 a(24)-a(27) from _Toshitaka Suzuki_, Jun 22 2025