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A235153
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Let x(1)x(2)... x(q) the decimal expansion of the numbers n having exactly q distinct prime divisors p(1)< p(2)< ... < p(q). Sequence lists the numbers n such that p(1)/x(q) + p(2)/x(q-1)+ ... + p(q)/x(1) is an integer.
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1
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2, 3, 5, 7, 12, 24, 48, 132, 222, 234, 266, 364, 418, 468, 555, 663, 666, 2418, 2442, 3498, 4218, 4422, 6216, 6314, 6612, 8844, 21714, 26796, 28842, 41412, 61446, 62634, 66234, 82824, 491946, 641886, 648186
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OFFSET
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1,1
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COMMENTS
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The sequence is finite because the smallest number with 11 distinct divisors is n = 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, 2, 1, 13, 21, 8, 11, 6, 16, 4, 9, 6, 7, 22, 23, 21, 22, 22, 13, 18, 12, 11, 39, 18, 17, 30, 17, 22, 22, 15, 30, 31, 25
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LINKS
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Table of n, a(n) for n=1..37.
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EXAMPLE
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26796 is in the sequence because the five prime divisors are {2, 3, 7, 11, 29} and 2/6 + 3/9 + 7/7 + 11/6 + 29/2 = 18.
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MAPLE
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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[i]', 'i'=1..n1):
if s=floor(s)
then
printf(`%d, `, n):
else
fi:
fi:
od:
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CROSSREFS
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Cf. A235152.
Sequence in context: A062713 A086108 A052430 * A177968 A024784 A060528
Adjacent sequences: A235150 A235151 A235152 * A235154 A235155 A235156
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KEYWORD
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nonn,base,fini
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AUTHOR
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Michel Lagneau, Jan 04 2014
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STATUS
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approved
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