A363537 Rewrite A087980(n) = Product_{i=1..m} p(i)^e(i) instead as Sum_{i=1..m} 2^(i-1), where m = omega(A087980(n)) = A001221(A087980(n)).
0, 1, 2, 4, 3, 8, 5, 16, 9, 32, 6, 17, 64, 10, 33, 128, 18, 7, 65, 12, 256, 34, 11, 129, 20, 512, 66, 19, 257, 36, 1024, 13, 130, 24, 35, 513, 68, 2048, 21, 258, 40, 67, 1025, 132, 4096, 37, 514, 72, 14, 131, 2049, 25, 260, 48, 8192, 69, 1026, 136, 22, 259, 4097, 41, 516, 80, 16384, 133, 2050, 264, 38
Offset: 1
Keywords
Examples
Table relating this sequence to A087980, where b(n) = A087980(n), f(n) = A067255(n), g(n) = A272011(n), and a(n)_2 the binary expansion of a(n): n b(n) f(b(n)) a(n) g(a(n)) a(n)_2 1 1 0 0 2 2 1 1 0 1 3 4 2 2 1 1. 4 8 3 4 2 1.. 5 12 2,1 3 1,0 11 6 16 4 8 3 1... 7 24 3,1 5 2,0 1.1 8 32 5 16 4 1.... 9 48 4,1 9 3,0 1..1 10 64 6 32 5 1..... 11 72 3,2 6 2,1 11. 12 96 5,1 17 4,0 1...1 13 128 7 64 6 1...... 14 144 4,2 10 3,1 1.1. 15 192 6,1 33 5,0 1....1 16 256 8 128 7 1....... 17 288 5,2 18 4,1 1..1. 18 360 3,2,1 7 2,1,0 111 ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..11157 (a(11157) = 2^64.)
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..1203278.
- Michael De Vlieger, Plot S(n,k) in row a(n) of A272011 at (x,y) = (n,k), n = 1..2048.
Programs
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Mathematica
m = 15; f[n_] := Times @@ MapIndexed[Prime[First[#2]]^(#1 + 1) &, Length[#] - Position[#, 1][[All, 1]]] &[IntegerDigits[n, 2]]; SortBy[Select[Array[{#, f[#]} &, 2^(m + 1)], Last[#] <= 2^m &], Last][[All, 1]]
Formula
a(2^k) = 2^(k-1) for k > 0.
a(A006939(k)) = 2^k-1 for k > 0.
Comments