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Composite numbers that are anagrams of the concatenation of their prime factors.
1

%I #15 May 20 2020 16:28:11

%S 735,1255,3792,7236,11913,12955,13175,17276,17482,19075,19276,23535,

%T 25105,32104,34112,37359,42175,100255,101299,104392,105295,107329,

%U 117067,117873,121325,121904,121932,123544,123678,124483,127417,129595,131832,132565,139925

%N Composite numbers that are anagrams of the concatenation of their prime factors.

%C The sequence contains two subsequences:

%C Subsequence 1: numbers with distinct digits. This finite subsequence begins with the numbers 735, 3792, 7236, 17482, 19075, 19276, 32104, ...

%C Subsequence 2: numbers with non-distinct digits. This subsequence begins with the numbers 1255, 11913, 12955, 13175, 17276, 23535, ...

%H Robert Israel, <a href="/A306474/b306474.txt">Table of n, a(n) for n = 1..500</a>

%e 3792 is in the sequence because the concatenation of the prime distinct divisors {2, 3, 79} is 2379, anagram of 3792.

%p with(numtheory):

%p for n from 1 to 140000 do:

%p if type(n,prime)=false

%p then

%p x:=factorset(n):n1:=nops(x): s:=0:s0:=0:

%p for i from n1 by -1 to 1 do:

%p a:=x[i]:b:=length(a):s:=s+a*10^s0:s0:=s0+b:

%p od:

%p if sort(convert(n, base, 10)) = sort(convert(s, base, 10))

%p then

%p printf(`%d, `, n):

%p else

%p fi:fi:

%p od:

%t Select[Range[2,140000],If [!PrimeQ[#],Sort@IntegerDigits@#==Sort[Join@@IntegerDigits[First/@FactorInteger[#]]]]&]

%Y Cf. A023086, A209799.

%Y A121342 is a subsequence.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Feb 18 2019