A355893 - OEIS

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.

0, 1, 10, 100, 2, 1000, 20, 10000, 100000, 1000000, 3, 10000000, 100000000, 200, 1010, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 4, 10000000000000000

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OFFSET

1,3

COMMENTS

A090252 and A354169 are similar in many ways. This sequence and A355892 illustrate this.

This compressed format only make sense if all e_i are less than 10, that is, for n <= 24574.

It is believed that 6 does not appear in A090252, so 11 is missing from the present sequence.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1073

FORMULA

a(n) = A054841(A090252(n)). - Stefano Spezia, Aug 24 2022

EXAMPLE

The initial terms of A090252 are:

1 -> 0

2 = 2^1 ->1

3 = 2^0 3^1 -> 10

5 = 2^0 3^0 5^1 -> 100

4 = 2^2 -> 2

7 = 2^0 3^0 5^0 7^1 -> 1000

9 = 2^0 3^2 -> 20

...

The terms, right-justified, for comparison with A355892, are:

.1 ...................................0

.2 ...................................1

.3 ..................................10

.4 .................................100

.5 ...................................2

.6 ................................1000

.7 ..................................20

.8 ...............................10000

.9 ..............................100000

10 .............................1000000

11 ...................................3

12 ............................10000000

13 ...........................100000000

14 .................................200

15 ................................1010

16 ..........................1000000000

17 .........................10000000000

18 ........................100000000000

19 .......................1000000000000

20 ......................10000000000000

21 .....................100000000000000

22 ....................1000000000000000

23 ...................................4

24 ...................10000000000000000

...

MATHEMATICA

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 *)

CROSSREFS

Cf. A054841, A090252, A354169.

See A354150 for indices of powers of 2 in A090252.

Sequence in context: A145644 A317055 A284200 * A228410 A119589 A316915

Adjacent sequences: A355890 A355891 A355892 * A355894 A355895 A355896

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 23 2022

STATUS

approved