A212667 Numbers n such that the sum of digits of n equals the concatenation of the distinct prime divisors of n.

2, 3, 5, 7, 2401, 4913, 655360, 3906250, 6553600, 39062500, 41943040, 65536000, 390625000, 419430400, 655360000, 3906250000, 4194304000, 6553600000, 27512614111, 39062500000, 41943040000, 65536000000, 271818611107, 390625000000, 419430400000

Offset: 1

Author

Michel Lagneau, May 23 2012

Keywords

• nonn
• base

Comments

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.

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

Examples

			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.
		

Crossrefs

Cf. A046017.

Programs

Maple

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: