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

1,1

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, ...

Links

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

Example

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

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[#]]]]&]

Crossrefs

Cf. A023086, A209799.

A121342 is a subsequence.

Sequence in context: A126556 A349870 A174456 * A250053 A227755 A096595

Adjacent sequences: A306471 A306472 A306473 * A306475 A306476 A306477

Keyword

nonn,base

Author

Michel Lagneau, Feb 18 2019

Status

approved