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A087134 Smallest number having exactly n divisors that are not greater than the number's greatest prime factor.

%I A087134 #32 Jun 01 2025 09:57:52
%S A087134 1,2,6,20,42,84,156,312,684,1020,1380,1860,3480,3720,4920,7320,10980,
%T A087134 14640,16920,21960,26280,34920,45720,59640,69840,89880,106680,125160,
%U A087134 145320,177240,213360,244440,269640,354480,320040,375480,435960,456120,531720,647640
%N A087134 Smallest number having exactly n divisors that are not greater than the number's greatest prime factor.
%C A087134 A087133(a(n))=n.
%C A087134 Also smallest number such that the n-th divisor is prime. - _Reinhard Zumkeller_, May 15 2006
%C A087134 From _David A. Corneth_, Jan 22 2019: (Start)
%C A087134 For the first 10000 terms except 1, a(n) is of the form A025487(k) * p where p is the smallest prime larger than the n-th divisor and, if the (n+1)-th divisor exists, less than that divisor.
%C A087134 This sequence isn't a sequence of indices of records to A087133 as it's not monotonically increasing; 354480 = a(34) > a(35) = 320040. (End)
%H A087134 David A. Corneth, <a href="/A087134/b087134.txt">Table of n, a(n) for n = 1..10000</a>
%H A087134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>
%H A087134 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreatestPrimeFactor.html">Greatest Prime Factor</a>
%e A087134 a(3) = A119313(1) = 6.
%t A087134 With[{s = Array[Function[{d, p}, LengthWhile[d, # < p &]] @@ {#, SelectFirst[Reverse@ #, PrimeQ]} &@ Divisors@ # &, 10^6]}, Array[FirstPosition[s, #][[1]] &, Max@ s + 1, 0]] (* _Michael De Vlieger_, Jan 23 2019 *)
%o A087134 (PARI) a087133(n) = if (n==1, 1, my(f = factor(n), gpf = f[#f~,1]); sumdiv(n, d, d <= gpf));
%o A087134 a(n) = my(k = 1); while (a087133(k) != n, k++); k; \\ _Michel Marcus_, Sep 21 2014
%Y A087134 Cf. A006530, A025487, A087133, A119311, A119312.
%Y A087134 See A221647 for other sequences giving the smallest number whose n-th divisor satisfies some condition.
%K A087134 nonn
%O A087134 1,2
%A A087134 _Reinhard Zumkeller_, Aug 17 2003
%E A087134 More terms from _Reinhard Zumkeller_, May 15 2006
%E A087134 More terms from _Michel Marcus_, Sep 21 2014