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

1,2

Comments

n and a(n) have the same parity.

Links

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

Formula

Algorithm:

1. factorize n;

2. order prime factors by decreasing size;

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

Example

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

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 *)

Crossrefs

In A084317 the order of factors is increasing.

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

Sequence in context: A361320 A037279 A163591 * A361581 A361580 A353975

Adjacent sequences: A085304 A085305 A085306 * A085308 A085309 A085310

Keyword

base,look,nonn

Author

Labos Elemer, Jun 27 2003

Extensions

Edited by Robert G. Wilson v, Jul 15 2003

Status

approved