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

1,1

Comments

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

Links

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

Example

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

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:

Prog

(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
(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

Crossrefs

Cf. A141468, A209799.

Sequence in context: A081062 A330136 A307589 * A119613 A154371 A172509

Adjacent sequences: A209797 A209798 A209799 * A209801 A209802 A209803

Keyword

nonn,base

Author

Michel Lagneau, Mar 13 2012

Status

approved