A306474 Composite numbers that are anagrams of the concatenation of their prime factors.

735, 1255, 3792, 7236, 11913, 12955, 13175, 17276, 17482, 19075, 19276, 23535, 25105, 32104, 34112, 37359, 42175, 100255, 101299, 104392, 105295, 107329, 117067, 117873, 121325, 121904, 121932, 123544, 123678, 124483, 127417, 129595, 131832, 132565, 139925

Offset: 1

Author

Michel Lagneau, Feb 18 2019

Keywords

• nonn
• base

Comments

The sequence contains two subsequences:

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

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A023086, A209799.

A121342 is a subsequence.

Programs

Maple

with(numtheory):
for n from 1 to 140000 do:
if type(n,prime)=false
  then
  x:=factorset(n):n1:=nops(x): s:=0:s0:=0:
    for i from n1 by -1 to 1 do:
     a:=x[i]:b:=length(a):s:=s+a*10^s0:s0:=s0+b:
    od:
      if sort(convert(n, base, 10)) = sort(convert(s, base, 10))
       then
        printf(`%d, `, n):
        else
      fi:fi:
     od:

Mathematica

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