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%I #40 Dec 24 2016 11:35:54
%S 2,11,3,20,101,12,1001,110,4,21,102,1010,10001,13,200,100001,30,1002,
%T 111,5,10010,1000001,1100,22,10000001,100010,103,1011,10002,120,
%U 100000001,14,2000,201,1000010,100002,31,10100,1003,10000010,1000000001,112,10000000001,1020,6,100100,10011,1000002
%N Let k_i be the multiplicity of prime(i) in the prime factorization of the n-th composite number C_n, and let k_i=0 if prime(i) is not a factor of C_n. Then a(n)=1*k_1+10*k_2+100*k_3+...+10^N*k_N, where N is the index of the largest prime factor in C_n.
%F a(n) = 1*k_1+10*k_2+100*k_3+...+10^N*k_N, where k_i is the exponent of prime(i) in the factorization of the n-th composite number C_n, k_i=0 if prime(i) is not a factor in C_n. Also, N is the index of the largest prime factor of C_n, so that C_n = Product_{i=1..N} prime(i)^k_i.
%e The 1st composite number is 4 = 2^2, so a(1)=2.
%e The 2nd composite number is 6 = 3^1*2^1, so a(2)=11.
%e The 3rd composite number is 8 = 2^3, so a(3)=3.
%e The 4th composite number is 9 = 3^2*2^0, so a(4)=20.
%e The 5th composite number is 10 = 5^1*3^0*2^1, so a(5)=101.
%e The 6th composite number is 12 = 3^1*2^2, so a(6)=12.
%e The 7th composite number is 14 = 7^1*5^0*3^0*2^1, so a(7)=1001.
%e The 8th composite number is 15 = 5^1*3^1*2^0, so a(8)=110.
%e The 9th composite number is 16 = 2^4, so a(9)=4.
%e The 10th composite number is 18 = 3^2*2^1, so a(10)=21.
%t Map[FromDigits@ Reverse@ Function[w, ReplacePart[#, Flatten@ Map[{PrimePi@ #1 -> #2} & @@ # &, w]] &@ ConstantArray[0, PrimePi@ Max@ w[[All, 1]]]]@ FactorInteger@ # &, Select[Range[4, 120], CompositeQ]] (* _Michael De Vlieger_, Dec 10 2016 *)
%Y Cf. A002808. Subset of A054841.
%K nonn,base
%O 1,1
%A _Marcus Kylén_, Dec 08 2016
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