A085308 -id:A085308 - cp's OEIS frontend

A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.

1, 2, 3, 2, 5, 32, 7, 2, 3, 52, 11, 32, 13, 72, 53, 2, 17, 32, 19, 52, 73, 112, 23, 32, 5, 132, 3, 72, 29, 532, 31, 2, 113, 172, 75, 32, 37, 192, 133, 52, 41, 732, 43, 112, 53, 232, 47, 32, 7, 52, 173, 132, 53, 32, 115, 72, 193, 292, 59, 532, 61, 312, 73, 2, 135, 1132, 67

Offset: 1

Labos Elemer, Jun 27 2003

n and a(n) have the same parity.

			m = 100 = 2*2*5*5 -> {2,5} -> {5,2} -> 52 = a(100);
a(510510) = 1713117532, while A084317(510510) = 2357111317.

Alois P. Heinz, Table of n, a(n) for n = 1..20000

In A084317 the order of factors is increasing.

Cf. A084317, A084318, A084319, A085308, A085309, A084796, A084797.

with(numtheory):
a:= n-> parse(cat(`if`(n=1, 1, sort([factorset(n)[]], `>`)[]))):
seq(a(n), n=1..100);  # Alois P. Heinz, May 02 2016

f[n_] := FromDigits[ Flatten[ IntegerDigits /@ Reverse[ Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]]]]; Table[ f[n], {n, 1, 70}]
Table[FromDigits[Flatten[IntegerDigits/@Reverse[FactorInteger[n][[All, 1]]]]],{n,90}] (* Harvey P. Dale, Oct 10 2017 *)

Algorithm:
factorize n;
order prime factors by decreasing size;
concatenate prime factors and interpret the result as a decimal number.

Edited by Robert G. Wilson v, Jul 15 2003

A085309 Initial values providing nontrivial cyclic attractor when function defined in A085307 is iterated.

Original entry on oeis.org

213, 323, 639, 713

Offset: 1

Labos Elemer, Jun 27 2003

			n=213 gives {213,713,3123,3473,15123,713},
n=323 gives {323,1917,713,3123,3473,15123,713},
n=639 gives {639,713,3123,3473,15123,713}.

Cf. A084317-A084319, A085307, A085308, A085309.

Algorithm: 1# factorize n; 2# arrange prime-factors by decreasing size; 3# concatenate prime factors and interpret the result as decimal number.Iterate 1#, 2#, 3#.

A084685 a(n) is the least x such that length of fixed-point-list when function-A085307[] was iterated and started at a(n) equals n.

Original entry on oeis.org

2, 4, 6, 14, 22, 115, 55, 105, 155, 145, 341, 501, 489, 143, 437, 301, 395, 665

Offset: 1

Labos Elemer, Jul 16 2003

			Some lists of iterated values started at a(n):
n=1: a(1)=first prime; n=2: a(2)=first true prime factor;
n=3: a(3)=first 2^j.3^i number, that is 6;
n=5: {22,112,72,32,2}
n=12: length=a(12); iv=501; fixed-point=1354674597313; list as follows
{501, 1673, 2397, 47173, 293237, 2571637, 23593109, 273116353, 522211523, 8866073119, 57914987307, 1354674597313}

Cf. A085307, A085308, A085309, A085317-A085323.

cp's OEIS Frontend

A085307 a(1) = 1; for n > 1, concatenate distinct prime factors of n in decreasing order.

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A085309 Initial values providing nontrivial cyclic attractor when function defined in A085307 is iterated.

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A084685 a(n) is the least x such that length of fixed-point-list when function-A085307[] was iterated and started at a(n) equals n.

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