OFFSET
1,32
COMMENTS
From an idea of Charles R Greathouse IV.
a(A211223(n)) > 0. - Reinhard Zumkeller, Jan 06 2013
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3)=1 because sigma(3)=sigma(1)+sigma(2)=4;
a(32)=2 because sigma(32)=sigma(4)+sigma(28)=sigma(14)+sigma(18)=63;
a(117)=3 because sigma(117)=sigma(41)+sigma(76)=sigma(52)+sigma(65)=sigma(56)+sigma(61)=182; etc.
MAPLE
MATHEMATICA
a[n_] := With[{s = DivisorSigma[1, n]}, Sum[Boole[s == DivisorSigma[1, x] + DivisorSigma[1, n-x]], {x, 1, Quotient[n, 2]}]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 04 2023 *)
PROG
(PARI) a(n)=my(t=sigma(n)); sum(i=1, n\2, sigma(i)+sigma(n-i)==t) \\ Charles R Greathouse IV, May 07 2012
(Haskell)
a211225 n = length $ filter (== a000203 n) $ zipWith (+) us' vs where
(us, vs@(v:_)) = splitAt (fromInteger $ (n - 1) `div` 2) a000203_list
us' = if even n then v : reverse us else reverse us
-- Reinhard Zumkeller, Jan 06 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, May 07 2012
STATUS
approved