A212667 - OEIS

%I #5 May 23 2012 20:02:07

%S 2,3,5,7,2401,4913,655360,3906250,6553600,39062500,41943040,65536000,

%T 390625000,419430400,655360000,3906250000,4194304000,6553600000,

%U 27512614111,39062500000,41943040000,65536000000,271818611107,390625000000,419430400000

%N Numbers n such that the sum of digits of n equals the concatenation of the distinct prime divisors of n.

%C The sequence is infinite because 3906250 = 2*5^9 is in the sequence => 2^(1+p) * 5^(9+p) = 39062500….0 is also in the sequence.

%C The prime numbers of A046017 are included in this sequence. For example A046017(4) = 7 => 7^4 = 2401 is in this sequence.

%e 655360 is in the sequence because 655360 = 2^17 * 5 => the concatenation of the prime divisors is the number 25 and 6+5+5+3+6+0 = 25.

%p with(numtheory):for n from 1 to 10^8 do: V:=convert(n, base, 10): n1:=nops(V): s1:=sum(‘V[m]’, ‘m’=1..n1):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 s=s1 then print(n):else fi:od:

%Y Cf. A046017.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, May 23 2012