A123132 - OEIS

%I #22 Feb 26 2024 01:56:27

%S 12,13,22,15,1213,17,32,23,1215,111,2213,113,1217,1315,42,117,1223,

%T 119,2215,1317,12111,123,3213,25,12113,33,2217,129,121315,131,52,

%U 13111,12117,1517,2223,137,12119,13113,3215,141,121317,143,22111,2315,12123

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

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

%H Paolo P. Lava, <a href="/A123132/b123132.txt">Table of n, a(n) for n = 2..10000</a>

%H A. Frank & P. Jacqueroux, <a href="http://www.paulcooijmans.com/others/intcontest.pdf">International Contest</a>, 2001.

%e 2 has "one 2" in its prime decomposition, so a(2)=12.

%e 3 has "one 3" in its prime decomposition, so a(3)=13.

%e 4=2*2 has "two 2" in its prime decomposition, so a(4)=22.

%e 5 has "one 5" in its prime decomposition, so a(5)=15.

%e 6=2*3 has "one 2 and one 3" in its prime decomposition, so a(6)=1213.

%e .....

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

%o (PARI) for(n=2,25,factn=factor(n); for(i=1,omega(n),print1(factn[i,2],factn[i,1])); print1(","))

%o (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

%Y Cf. A006751, A027746, A063850.

%K nonn,base

%O 2,1

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