OFFSET
1,2
COMMENTS
The name contains an unmatched parenthesis. - Editors, Mar 12 2024
FORMULA
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)
a(2^n) = A000225(n+1). - R. J. Mathar, Mar 13 2024
A038712(n) | a(n). - R. J. Mathar, Mar 13 2024
EXAMPLE
SPM4Sigma(240) = (1+2+4+8+16)*(-1+3)*(1+5).
MAPLE
A126851 := proc(n)
local r, mprime, piri, iprod, pi, ri, si;
r := A007814(n) ;
mprime := n/2^r ;
iprod := 1 ;
if mprime > 1 then
for piri in ifactors(mprime)[2] do
pi := op(1, piri) ;
ri := op(2, piri) ;
add(pi^si, si=1..ri) + (-1)^( (pi-1)/2) ;;
iprod := iprod*% ;
end do:
end if;
%*A038712(n) ;
end proc:
seq(A126851(n), n=1..40) ; # R. J. Mathar, Mar 13 2024
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Yasutoshi Kohmoto, Feb 24 2007
EXTENSIONS
a(2) and a(7) corrected, sequence extended beyond a(20). - R. J. Mathar, Mar 13 2024
STATUS
approved