A235152 Let x(1)x(2)...x(q) the decimal expansion of the numbers k having exactly q distinct prime divisors p(1) < p(2) < ... < p(q). Sequence lists the numbers k such that p(1)/x(1) + p(2)/x(2) + ... + p(q)/x(q) is an integer.

2, 3, 5, 7, 15, 222, 555, 666, 834, 1122, 2442, 3162, 4818, 6162, 6216, 8274, 8554, 28842, 49266, 49434, 61446, 69762, 83334, 88638, 88842, 89838, 641886, 648186, 795795, 892164

Offset

1,1

Comments

The sequence is finite because the smallest number with 11 distinct divisors is k = 2*3*5*7*11*13*17*19*23*29*31 = 200560490130 with 12 decimal digits.

The corresponding integers are 1, 1, 1, 1, 4, 21, 9, 7, 36, 19, 23, 22, 21, 45, 15, 52, 16, 19, 11, 33, 11, 79, 24, 18, 40, 13, 19, 26, 16, 31.

Links

Table of n, a(n) for n=1..30.

Example

28842 is in the sequence because the five prime divisors are {2, 3, 11, 19, 23} and  2/2 + 3/8 + 11/8 + 19/4 + 23/2 = 19.

Maple

with(numtheory):
   for n from 1 to 1000000 do:
      x:=convert(n, base, 10):
      n1:=nops(x):
      p:=product('x[i]', 'i'=1..n1):
      y:=factorset(n):
      n2:=nops(y):
        if p<>0 and n1=n2
         then
         s:=sum('y[i]/x[n1-i+1]', 'i'=1..n1):
          if s=floor(s)
           then
           printf(`%d, `, n):
           else
          fi:
        fi:
      od:

Prog

(PARI) is(k) = {my(d=digits(k), f=factor(k)[, 1], x); (x=#d)==#f && vecmin(d) && denominator(sum(i=1, x, f[i]/d[i]))==1; } \\ Jinyuan Wang, Mar 27 2020

Crossrefs

Cf. A235153.

Sequence in context: A079987 A085547 A058702 * A363720 A024377 A025069

Adjacent sequences: A235149 A235150 A235151 * A235153 A235154 A235155

Keyword

nonn,base,fini,full

Author

Michel Lagneau, Jan 04 2014

Status

approved