A123132 Describe prime factorization of n (primes in ascending order and with repetition) (method A - initial term is 2).

12, 13, 22, 15, 1213, 17, 32, 23, 1215, 111, 2213, 113, 1217, 1315, 42, 117, 1223, 119, 2215, 1317, 12111, 123, 3213, 25, 12113, 33, 2217, 129, 121315, 131, 52, 13111, 12117, 1517, 2223, 137, 12119, 13113, 3215, 141, 121317, 143, 22111, 2315, 12123

Offset

2,1

Comments

Method A = 'frequency' followed by 'digit'-indication. Say 'what you see' in prime factors of n, n>1.

Links

Paolo P. Lava, Table of n, a(n) for n = 2..10000

A. Frank & P. Jacqueroux, International Contest, 2001.

Example

2 has "one 2" in its prime decomposition, so a(2)=12.
3 has "one 3" in its prime decomposition, so a(3)=13.
4=2*2 has "two 2" in its prime decomposition, so a(4)=22.
5 has "one 5" in its prime decomposition, so a(5)=15.
6=2*3 has "one 2 and one 3" in its prime decomposition, so a(6)=1213.
.....

Mathematica

a[n_] := FromDigits@ Flatten@ IntegerDigits[ Reverse /@ FactorInteger@ n]; a/@ Range[2, 30] (* Giovanni Resta, Jun 16 2013 *)

Prog

(PARI) for(n=2, 25, factn=factor(n); for(i=1, omega(n), print1(factn[i, 2], factn[i, 1])); print1(", "))
(PARI) a(n) = my(factn=factor(n), sout = ""); for(i=1, omega(n), sout = concat(sout, Str(factn[i, 2])); sout = concat(sout, Str(factn[i, 1]))); eval(sout); \\ Michel Marcus, Jun 29 2017

Crossrefs

Cf. A006751, A027746, A063850.

Sequence in context: A105733 A035123 A140212 * A050840 A108710 A108709

Adjacent sequences: A123129 A123130 A123131 * A123133 A123134 A123135

Keyword

nonn,base

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006

Status

approved