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Numbers n such that the concatenation of the distinct prime divisors of n is composite.
1

%I #21 Mar 16 2023 12:23:13

%S 10,14,15,20,26,28,30,34,35,38,40,42,45,50,52,55,56,57,60,62,65,68,69,

%T 74,75,76,77,78,80,84,85,86,87,90,91,94,95,98,100,102,104,105,106,110,

%U 112,114,118,119,120,122,123,124,126,129,130,134,135,136,138,143

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

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

%H Charles R Greathouse IV, <a href="/A209800/b209800.txt">Table of n, a(n) for n = 1..10000</a>

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

%p 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:

%o (Magma) [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

%o (PARI) cat(n)=my(f=factor(n),s="");for(i=1,#f[,1],s=Str(s,f[i,1]));eval(s)

%o 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

%Y Cf. A141468, A209799.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Mar 13 2012