This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126851 #16 Mar 13 2024 19:28:01
%S A126851 1,3,2,7,6,6,6,15,11,18,10,14,14,18,12,31,18,33,18,42,12,30,22,30,31,
%T A126851 42,38,42,30,36,30,63,20,54,36,77,38,54,28,90,42,36,42,70,66,66,46,62,
%U A126851 55,93,36,98,54,114,60,90,36,90,58,84,62,90,66,127,84,60,66,126,44,108,70,165,74,114,62,126,60,84,78,186
%N A126851 SPM4Sigma(n) = (-1)^(1/2*((Sum_i p_i)-Omega(m'))*Sum_{d|n} (-1)^(1/2*((Sum_j p_j)-Omega(d'))*d =(2^(r+1)-1)*Product_i [Sum_{1<=s_i<=r_i} p_i^s_i +(-1)^((p_i-1)/2)] where n=2^r*m', gcd(2,m')=1, m'=Product_i p_i^r_i, d=2^k*d', gcd(2,d')=1, d'=Product_j p_j^r_j SPM4 for Signed by Prime factors Mod 4.
%C A126851 The name contains an unmatched parenthesis. - Editors, Mar 12 2024
%F A126851 SPM4Sigma(n) = (2^r-1)*Product_i (p_i^(r_i+1)-p_i)/(p_i-1)+(-1)^(1/2*(p_i-1)) = (2^r-1)*Product_{i=1 mod 4} ((p_i^(r_i+1)-p_i)/(p_i-1)+1)*Product_{i=3 mod 4} ((p_i^(r_i+1)-p_i)/(p_i-1)-1)
%F A126851 a(2^n) = A000225(n+1). - _R. J. Mathar_, Mar 13 2024
%F A126851 A038712(n) | a(n). - _R. J. Mathar_, Mar 13 2024
%e A126851 SPM4Sigma(240) = (1+2+4+8+16)*(-1+3)*(1+5).
%p A126851 A126851 := proc(n)
%p A126851 local r,mprime,piri,iprod,pi,ri,si;
%p A126851 r := A007814(n) ;
%p A126851 mprime := n/2^r ;
%p A126851 iprod := 1 ;
%p A126851 if mprime > 1 then
%p A126851 for piri in ifactors(mprime)[2] do
%p A126851 pi := op(1,piri) ;
%p A126851 ri := op(2,piri) ;
%p A126851 add(pi^si,si=1..ri) + (-1)^( (pi-1)/2) ;;
%p A126851 iprod := iprod*% ;
%p A126851 end do:
%p A126851 end if;
%p A126851 %*A038712(n) ;
%p A126851 end proc:
%p A126851 seq(A126851(n),n=1..40) ; # _R. J. Mathar_, Mar 13 2024
%Y A126851 Cf. A126852.
%K A126851 nonn,uned
%O A126851 1,2
%A A126851 _Yasutoshi Kohmoto_, Feb 24 2007
%E A126851 a(2) and a(7) corrected, sequence extended beyond a(20). - _R. J. Mathar_, Mar 13 2024