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

Author

Labos Elemer, Jun 27 2003

Keywords

• base
• look
• nonn

Comments

n and a(n) have the same parity.

Examples

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

Links

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

Crossrefs

In A084317 the order of factors is increasing.

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

Programs

Maple

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

Mathematica

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 *)

Formula

Algorithm:

1. factorize n;

2. order prime factors by decreasing size;

3. concatenate prime factors and interpret the result as a decimal number.

Extensions

Edited by Robert G. Wilson v, Jul 15 2003