Search: id:A115156
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%I A115156
%S A115156 2,6,28,54,405,486,2808,4860,21870,40824,192456,524160,708588,4059072,
%T A115156 14348907,58576608,123731712,462944160,1837080000,3874204890,
%U A115156 11809800000,48183984000,65086642152,339033848832
%N A115156 Smallest number having exactly n ones in binary representation and also 
               exactly n prime factors (counted with multiplicity).
%C A115156 A001222(a(n)) = A000120(a(n)) = n; subsequence of A071814.
%C A115156 a(n) is roughly 3^n and so far 4 <= a(n)/3^(n-2) <= 15. - Robert G. Wilson 
               v.
%e A115156 a(5) = 3*3*3*3*5 = 405_10 = 110010101_2.
%e A115156 a(10) = 2*2*2*3*3*3*3*3*3*7 = 40824_10 = 1001111101111000_2.
%e A115156 a(18) = 2*2*2*2*2*3*3*3*3*3*3*3*3*3*3*5*7*7 = 462944160_10 = 11011100101111111011110100000_2. 
               (Robert G. Wilson v)
%t A115156 Lk[n_] := Block[{k = 2^n - 1}, While[n != Plus @@ IntegerDigits[k, 2] 
               || n != Plus @@ (Transpose[FactorInteger@k][[2]]), k++ ]; k]; L = 
               {}; Do[v = Lk[n]; Print[{n, v}]; AppendTo[L, v], {n, 2, 16}]; L (Resta)
%t A115156 t = Table[0, {20}]; f[n_] := Block[{b = Count[ IntegerDigits[n, 2], 1], 
               e = Plus @@ Last /@ FactorInteger@n}, If[b == e, b, 0]]; Do[ a = 
               f@n; If[a > 0 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 550000000}]; 
               t (* Robert G. Wilson v *)
%t A115156 f[n_] := Min[ Select[ FromDigits[ #, 2] & /@ Permutations[ Join[ Table[0, 
               {Max[6, 2n/3]}], Table[1, {n}]]], Plus @@ Last /@ FactorInteger@# 
               == n &]]; Array[f, 18] (* Robert G. Wilson v *)
%Y A115156 Sequence in context: A153253 A074925 A141136 this_sequence A089748 A047125 
               A065577
%Y A115156 Adjacent sequences: A115153 A115154 A115155 this_sequence A115157 A115158 
               A115159
%K A115156 nonn
%O A115156 1,1
%A A115156 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 14 2006
%E A115156 a(14)-a(17) from Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 18 2006
%E A115156 a(14)-a(18) from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 18 2006
%E A115156 a(19) from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 22 2006
%E A115156 a(20)-a(24) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 
               07 2008

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