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Search: id:A115156
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| A115156 |
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Smallest number having exactly n ones in binary representation and also exactly n prime factors (counted with multiplicity). |
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+0
3
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| 2, 6, 28, 54, 405, 486, 2808, 4860, 21870, 40824, 192456, 524160, 708588, 4059072, 14348907, 58576608, 123731712, 462944160, 1837080000, 3874204890, 11809800000, 48183984000, 65086642152, 339033848832
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A001222(a(n)) = A000120(a(n)) = n; subsequence of A071814.
a(n) is roughly 3^n and so far 4 <= a(n)/3^(n-2) <= 15. - Robert G. Wilson v.
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EXAMPLE
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a(5) = 3*3*3*3*5 = 405_10 = 110010101_2.
a(10) = 2*2*2*3*3*3*3*3*3*7 = 40824_10 = 1001111101111000_2.
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)
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MATHEMATICA
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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 = 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 *)
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 *)
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CROSSREFS
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Adjacent sequences: A115153 A115154 A115155 this_sequence A115157 A115158 A115159
Sequence in context: A153253 A074925 A141136 this_sequence A089748 A047125 A065577
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 14 2006
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EXTENSIONS
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a(14)-a(17) from Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 18 2006
a(14)-a(18) from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 18 2006
a(19) from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 22 2006
a(20)-a(24) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 07 2008
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