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
Examples
105 is in the sequence because the prime distinct divisors of 105 are {3,5,7} and 357 = 3*7*17 is composite.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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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
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Maple
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:
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PARI
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
Comments