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.
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
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Jan 04 2014
STATUS
approved