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A111303
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Numbers n such that 2^tau(n) = n + 1 (where tau(n) = number of divisors of n).
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0
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OFFSET
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1,2
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COMMENTS
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It is clear that n+1 must be a power of 2. Hence n=2^k-1 for some k. Found k=1, 2, 4, 6, 8, 16, 32. No other k<150. - T. D. Noe, Nov 04 2005
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LINKS
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FORMULA
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Note that this is different from the sequence A019434 - 2.
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MATHEMATICA
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Select[Range[10^6], 2^DivisorSigma[0, # ] == # + 1 &]
2^Select[Range[150], DivisorSigma[0, 2^#-1]==#&] - 1 (Noe)
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PROG
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(Python)
from sympy import divisor_count as tau
def afind(klimit, kstart=1):
for k in range(kstart, klimit+1):
m = 2**k - 1
if 2**tau(m) == m + 1: print(m, end=", ")
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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