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

1,1

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.

Links

Table of n, a(n) for n=1..25.

Example

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.

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:

Crossrefs

Cf. A046017.

Sequence in context: A224164 A224398 A066306 * A252357 A037948 A007659

Adjacent sequences: A212664 A212665 A212666 * A212668 A212669 A212670

Keyword

nonn,base

Author

Michel Lagneau, May 23 2012

Status

approved