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A055079 Smallest number with exactly n nonprime divisors.

%I A055079 #16 Mar 04 2024 19:36:59
%S A055079 1,4,8,12,30,24,36,48,60,72,2048,192,120,216,180,288,240,432,576,420,
%T A055079 360,864,1296,900,960,1728,720,840,1080,3456,9216,1260,1440,6912,
%U A055079 34359738368,1680,2160,10368,2880,15552,15360,3600,4620,2520,4320,31104
%N A055079 Smallest number with exactly n nonprime divisors.
%C A055079 a(n)<=2^n; see A057838 for the indices n where a(n)=2^n.
%H A055079 Ray Chandler, <a href="/A055079/b055079.txt">Table of n, a(n) for n=1..4438</a>
%F A055079 a(n)=Min{k; A000005(k)-A001221(k)=A033273(k)=n}
%e A055079 a(5) = 30 because it is the first integer which has five nonprime divisors (1, 6, 10, 15 and 30; the divisors 2, 3 and 5 are prime).
%e A055079 a(35) = 2^35 = 34359738368.
%e A055079 a(71) = 2^71 = 2361183241434822606848.
%e A055079 a(191) = 2^191 = 3138550867693340381917894711603833208051177722232017256448.
%t A055079 a = Table[0, {100} ]; Do[ c = Count[ PrimeQ[ Divisors[ n ] ], False]; If[ c < 101 && a[[ c ]] == 0, a[[ c ]] = n], {n, 2, 10077696} ];
%t A055079 Table[SelectFirst[Table[{n,Count[Divisors[n],_?(!PrimeQ[#]&)]},{n,10000}],#[[2]]==k&],{k,34}][[;;,1]] (* The program generates the first 34 terms of the sequence. *) (* _Harvey P. Dale_, Mar 04 2024 *)
%o A055079 (PARI) sme(n) = {k = 1; while (sumdiv(k, d, ! isprime(d)) != n, k++); k;} \\ _Michel Marcus_, Dec 13 2013
%o A055079 (Haskell)
%o A055079 a055079 n = head [x | x <- [1..], a033273 x == n]
%o A055079 -- _Reinhard Zumkeller_, Dec 16 2013
%Y A055079 Cf. A001221, A001222, A058060, A058061, A000005, A033273, A057838.
%K A055079 nonn,nice
%O A055079 1,2
%A A055079 _Labos Elemer_, Jun 13 2000
%E A055079 More terms from _Robert G. Wilson v_, Nov 20 2000
%E A055079 Edited by _Ray Chandler_, Aug 12 2010