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A339916
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The sum of 2^((d-1)/2) over all divisors of 2n+1.
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4
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1, 3, 5, 9, 19, 33, 65, 135, 257, 513, 1035, 2049, 4101, 8211, 16385, 32769, 65571, 131085, 262145, 524355, 1048577, 2097153, 4194455, 8388609, 16777225, 33554691, 67108865, 134217765, 268435971, 536870913, 1073741825, 2147484699, 4294967365, 8589934593, 17179871235, 34359738369, 68719476737
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OFFSET
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0,2
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COMMENTS
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This is sort of a bitmap representation of the divisors of odd numbers.
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LINKS
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EXAMPLE
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For n=7, a(7)=2^7+2^2+2^1+2^0=135 because the divisors of 15 are 15,5,3,1.
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MAPLE
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seq(add(2^((d-1)/2), d=numtheory:-divisors(2*n+1)), n=0..100); # Robert Israel, Dec 24 2020
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MATHEMATICA
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A339916[n_]:=Block[{d=Divisors[2n+1]}, Sum[2^((d[[k]]-1)/2), {k, Length[d]}]]; Array[A339916, 50, 0]
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PROG
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(PARI) a(n) = sumdiv(2*n+1, d, 2^((d-1)/2)); \\ Michel Marcus, Dec 23 2020
(Python)
from sympy import divisors
def a(n): return sum(2**((d-1)//2) for d in divisors(2*n+1))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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