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A147806
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Partial sums of A147809(n) = tau(n^2 + 1)/2 - 1.
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2
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0, 0, 1, 1, 2, 2, 4, 5, 6, 6, 7, 8, 11, 11, 12, 12, 15, 17, 18, 18, 21, 22, 25, 25, 26, 26, 29, 30, 31, 32, 35, 37, 40, 41, 42, 42, 45, 47, 48, 48, 50, 51, 56, 57, 58, 59, 66, 67, 68, 69, 70, 71, 74, 74, 77, 77, 84, 85, 86, 87, 88, 89, 92, 93, 94, 94, 97, 100, 101, 103, 104, 107
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OFFSET
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1,5
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COMMENTS
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It seems that a(10^n) = (6, 168, 2754, 38561, 495569, ...) ~ 1.1*(n-0.5)*10^n; otherwise said, a(n) ~ 1.1*(log_10(n)-0.5)*n, asymptotically.
The exact value of the coefficient above is 3* log(10)/(2*Pi)) = 1.09940339... . - Amiram Eldar, Dec 01 2023
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LINKS
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FORMULA
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MATHEMATICA
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Accumulate[DivisorSigma[0, Range[72]^2 + 1]/2 - 1] (* Amiram Eldar, Oct 25 2019 *)
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PROG
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(PARI) s=0; a147806=vector(99, n, s+=numdiv(n^2+1))/2
A147806(n)=sum(p=1, n, numdiv(n^2+1))/2-n
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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