A209799 -id:A209799 - cp's OEIS frontend

A209800 Numbers n such that the concatenation of the distinct prime divisors of n is composite.

10, 14, 15, 20, 26, 28, 30, 34, 35, 38, 40, 42, 45, 50, 52, 55, 56, 57, 60, 62, 65, 68, 69, 74, 75, 76, 77, 78, 80, 84, 85, 86, 87, 90, 91, 94, 95, 98, 100, 102, 104, 105, 106, 110, 112, 114, 118, 119, 120, 122, 123, 124, 126, 129, 130, 134, 135, 136, 138, 143

Offset: 1

Michel Lagneau, Mar 13 2012

Concatenation is done with smaller factors to the left of larger factors.

			105 is in the sequence because the prime distinct divisors of 105 are {3,5,7} and 357 = 3*7*17 is composite.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A141468, A209799.

[n: n in [2..144] | not IsPrime(t) where t is Seqint(Reverse(&cat[Reverse(Intseq(PrimeDivisors(n)[k])): k in [1..#PrimeDivisors(n)]]))]; // Bruno Berselli, Mar 20 2012

with(numtheory):for n from 1 to 200 do: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 type(s,prime)=false then printf(`%d, `,n):else fi:od:

cat(n)=my(f=factor(n),s="");for(i=1,#f[,1],s=Str(s,f[i,1]));eval(s)
p=7;forprime(q=11,1e3,for(n=p+1,q-1,if(!isprime(cat(n)),print1(n", ")));p=q) \\ Charles R Greathouse IV, Mar 20 2012

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

Original entry on oeis.org

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

Michel Lagneau, Feb 18 2019

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, ...

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

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

Cf. A023086, A209799.

A121342 is a subsequence.

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:

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

A287916 Numbers m such that the decimal digits of m are exactly the same as those of all the indices corresponding to the prime factors of m.

Original entry on oeis.org

12, 14, 123, 154, 2127, 2391, 3614, 4031, 5318, 7174, 8491, 11142, 12435, 12830, 18126, 20314, 23514, 24612, 25201, 28731, 31934, 42158, 50314, 51124, 61411, 62116, 65315, 72401, 73201, 81254, 81372, 92315, 93243, 112924, 123126, 123612, 123861, 124341, 125102

Offset: 1

Michel Lagneau, Jul 11 2017

The sequence contains two subsequences:
Subsequence 1: numbers with distinct digits. This finite subsequence begins with the numbers 12, 14, 123, 154, 2391, 3614, 4031, 5318, 8491, 12435, 12830, 23514, ... (see example 1)
Subsequence 2: numbers with non-distinct digits (see example 2). This subsequence begins with the numbers 2127, 7174, 11142, 18126, ...

			12435 is in the sequence because the prime factors are {3, 5, 829} with 3 = prime(2), 5 = prime(3) and 829 = prime(145). The decimal digits corresponding to the indices {2, 3, 145} of the prime divisors are the same as the digits of the number 12435.
61411 is in the sequence because the prime factors are {7, 31, 283} with 7 = prime(4), 31 = prime(11) and 283 = prime(61). The decimal digits corresponding to the indices {4, 11, 61} are the same as the digits of the number 61411.

Cf. A121342, A209799.

with(numtheory):nn:=200000:
for n from 10 to nn do:
  x:=convert(n,base,10):n0:=nops(x):U:=array(0..9,[0$10]):
   for a from 1 to n0 do:
    U[x[a]]:=U[x[a]]+1:
   od:
   y:=factorset(n):n1:=nops(y):V:=array(0..9,[0$10]):
  for i from 1 to n1 do :
    p:=y[i]:ii:=0:
      for k from 1 to 10000 while(ii=0) do:
        if ithprime(k) = p
        then
        ii:=1:z:=convert(k,base,10):nz:=nops(z):
           for b from 1 to nz do:
            V[z[b]]:=V[z[b]]+1:
           od:
        else
        fi:
      od:
     od:
       jj:=0:
       for b from 0 to 9 do:
        if U[b]<>V[b] then jj:=1:
        else fi:
       od:
        if jj=0
         then print(n):
         else fi:
     od:

Select[Range[125102], Sort@ IntegerDigits@ # == Sort[Join @@ IntegerDigits[ PrimePi[ First /@ FactorInteger[#]]]] &] (* Giovanni Resta, Jul 11 2017 *)

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A209800 Numbers n such that the concatenation of the distinct prime divisors of n is composite.

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

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A287916 Numbers m such that the decimal digits of m are exactly the same as those of all the indices corresponding to the prime factors of m.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Mathematica