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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.
1
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.
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
KEYWORD
nonn,base,fini,full
AUTHOR
Michel Lagneau, Jan 04 2014
STATUS
approved