A147806 Partial sums of A147809(n) = tau(n^2 + 1)/2 - 1.

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

Offset

1,5

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A147807(n) - n.

a(n) ~ c * n * log(n), where c = 3/(2*Pi) = 0.477464... (A093582). - Amiram Eldar, Dec 01 2023

Mathematica

Accumulate[DivisorSigma[0, Range[72]^2 + 1]/2 - 1] (* Amiram Eldar, Oct 25 2019 *)

Prog

(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

Crossrefs

Cf. A093582, A147807, A147809, A147810, A147811.

Sequence in context: A181537 A130498 A263433 * A338228 A351782 A064574

Adjacent sequences: A147803 A147804 A147805 * A147807 A147808 A147809

Keyword

easy,nonn

Author

M. F. Hasler, Dec 13 2008

Status

approved