cp's OEIS Frontend

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

%I A147806 #19 Oct 04 2024 06:21:24
%S A147806 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,
%T A147806 30,31,32,35,37,40,41,42,42,45,47,48,48,50,51,56,57,58,59,66,67,68,69,
%U A147806 70,71,74,74,77,77,84,85,86,87,88,89,92,93,94,94,97,100,101,103,104,107
%N A147806 Partial sums of A147809(n) = tau(n^2 + 1)/2 - 1.
%C A147806 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.
%C A147806 The exact value of the coefficient above is 3*log(10)/(2*Pi) = 1.09940339... . - _Amiram Eldar_, Dec 01 2023
%H A147806 Amiram Eldar, <a href="/A147806/b147806.txt">Table of n, a(n) for n = 1..10000</a>
%F A147806 a(n) = A147807(n) - n.
%F A147806 a(n) ~ c * n * log(n), where c = 3/(2*Pi) = 0.477464... (A093582). - _Amiram Eldar_, Dec 01 2023
%t A147806 Accumulate[DivisorSigma[0, Range[72]^2 + 1]/2 - 1] (* _Amiram Eldar_, Oct 25 2019 *)
%o A147806 (PARI) s=0;a147806=vector(99,n,s+=numdiv(n^2+1))/2
%o A147806 A147806(n)=sum(p=1,n,numdiv(n^2+1))/2-n
%Y A147806 Cf. A093582, A147807, A147809, A147810, A147811.
%K A147806 easy,nonn
%O A147806 1,5
%A A147806 _M. F. Hasler_, Dec 13 2008