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%I #33 Aug 24 2022 12:01:47
%S 0,1,10,100,2,1000,20,10000,100000,1000000,3,10000000,100000000,200,
%T 1010,1000000000,10000000000,100000000000,1000000000000,
%U 10000000000000,100000000000000,1000000000000000,4,10000000000000000
%N Let A090252(n) = Product_{i >= 1} prime(i)^e(i); then a(n) is the concatenation, in reverse order, of e_1, e_2, ..., ending at the exponent of the largest prime factor of A090252(n); a(1)=0 by convention.
%C A090252 and A354169 are similar in many ways. This sequence and A355892 illustrate this.
%C This compressed format only make sense if all e_i are less than 10, that is, for n <= 24574.
%C It is believed that 6 does not appear in A090252, so 11 is missing from the present sequence.
%H Michael De Vlieger, <a href="/A355893/b355893.txt">Table of n, a(n) for n = 1..1073</a>
%F a(n) = A054841(A090252(n)). - _Stefano Spezia_, Aug 24 2022
%e The initial terms of A090252 are:
%e 1 -> 0
%e 2 = 2^1 ->1
%e 3 = 2^0 3^1 -> 10
%e 5 = 2^0 3^0 5^1 -> 100
%e 4 = 2^2 -> 2
%e 7 = 2^0 3^0 5^0 7^1 -> 1000
%e 9 = 2^0 3^2 -> 20
%e ...
%e The terms, right-justified, for comparison with A355892, are:
%e .1 ...................................0
%e .2 ...................................1
%e .3 ..................................10
%e .4 .................................100
%e .5 ...................................2
%e .6 ................................1000
%e .7 ..................................20
%e .8 ...............................10000
%e .9 ..............................100000
%e 10 .............................1000000
%e 11 ...................................3
%e 12 ............................10000000
%e 13 ...........................100000000
%e 14 .................................200
%e 15 ................................1010
%e 16 ..........................1000000000
%e 17 .........................10000000000
%e 18 ........................100000000000
%e 19 .......................1000000000000
%e 20 ......................10000000000000
%e 21 .....................100000000000000
%e 22 ....................1000000000000000
%e 23 ...................................4
%e 24 ...................10000000000000000
%e ...
%t nn = 24, s = Import["https://oeis.org/A090252/b090252.txt", "Data"][[1 ;; nn, -1]]; f[n_] := If[n == 1, 0, Function[g, FromDigits@ Reverse@ ReplacePart[Table[0, {PrimePi[g[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, g]]@ FactorInteger@ n]; Array[f[s[[#]]] &, nn] (* _Michael De Vlieger_, Aug 24 2022 *)
%Y Cf. A054841, A090252, A354169.
%Y See A354150 for indices of powers of 2 in A090252.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Aug 23 2022
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