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A355893 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.

%I A355893 #33 Aug 24 2022 12:01:47
%S A355893 0,1,10,100,2,1000,20,10000,100000,1000000,3,10000000,100000000,200,
%T A355893 1010,1000000000,10000000000,100000000000,1000000000000,
%U A355893 10000000000000,100000000000000,1000000000000000,4,10000000000000000
%N A355893 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 A355893 A090252 and A354169 are similar in many ways. This sequence and A355892 illustrate this.
%C A355893 This compressed format only make sense if all e_i are less than 10, that is, for n <= 24574.
%C A355893 It is believed that 6 does not appear in A090252, so 11 is missing from the present sequence.
%H A355893 Michael De Vlieger, <a href="/A355893/b355893.txt">Table of n, a(n) for n = 1..1073</a>
%F A355893 a(n) = A054841(A090252(n)). - _Stefano Spezia_, Aug 24 2022
%e A355893 The initial terms of A090252 are:
%e A355893 1 -> 0
%e A355893 2 = 2^1 ->1
%e A355893 3 = 2^0 3^1 -> 10
%e A355893 5 = 2^0 3^0 5^1 -> 100
%e A355893 4 = 2^2 -> 2
%e A355893 7 = 2^0 3^0 5^0 7^1 -> 1000
%e A355893 9 = 2^0 3^2 -> 20
%e A355893 ...
%e A355893 The terms, right-justified, for comparison with A355892, are:
%e A355893 .1 ...................................0
%e A355893 .2 ...................................1
%e A355893 .3 ..................................10
%e A355893 .4 .................................100
%e A355893 .5 ...................................2
%e A355893 .6 ................................1000
%e A355893 .7 ..................................20
%e A355893 .8 ...............................10000
%e A355893 .9 ..............................100000
%e A355893 10 .............................1000000
%e A355893 11 ...................................3
%e A355893 12 ............................10000000
%e A355893 13 ...........................100000000
%e A355893 14 .................................200
%e A355893 15 ................................1010
%e A355893 16 ..........................1000000000
%e A355893 17 .........................10000000000
%e A355893 18 ........................100000000000
%e A355893 19 .......................1000000000000
%e A355893 20 ......................10000000000000
%e A355893 21 .....................100000000000000
%e A355893 22 ....................1000000000000000
%e A355893 23 ...................................4
%e A355893 24 ...................10000000000000000
%e A355893 ...
%t A355893 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 A355893 Cf. A054841, A090252, A354169.
%Y A355893 See A354150 for indices of powers of 2 in A090252.
%K A355893 nonn
%O A355893 1,3
%A A355893 _N. J. A. Sloane_, Aug 23 2022