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Smallest Zuckerman number (A007602) with exactly n distinct prime factors.
2

%I #20 Jan 29 2023 09:39:36

%S 1,2,6,132,3276,27132,1117116,111914712,6111417312,1113117121116,

%T 1112712811322112,11171121131111172

%N Smallest Zuckerman number (A007602) with exactly n distinct prime factors.

%H Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Zuckerman_number/">Zuckerman numbers</a>, Numbers Aplenty.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DistinctPrimeFactors.html">Distinct Prime Factors</a>.

%e 3276 = 2^2*3^2*7*13 is the smallest integer with 4 distinct prime factors that is also Zuckerman number as 3276 / (3*2*7*6) = 13, so a(4) = 3276.

%o (PARI) a(n) = my(k=1); while (!(p=vecprod(digits(k))) || (k % p) || (omega(k) != n), k++); k; \\ _Michel Marcus_, Jan 21 2023

%Y Cf. A007602, A288069.

%Y Similar: A060319 (Fibonacci), A083002 (oblong), A359960 (Niven).

%K nonn,base,more

%O 0,2

%A _Bernard Schott_, Jan 21 2023

%E a(6)-a(7) from _Michel Marcus_, Jan 21 2023

%E a(8)-a(9) from _Daniel Suteu_, Jan 21 2023

%E a(10)-a(11) from _Bert Dobbelaere_, Jan 29 2023