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A211225 Number of ways to represent sigma(n) as sigma(x) + sigma(y) where x+y = n. 8
0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2 (list; graph; refs; listen; history; text; internal format)
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

with(numtheory);

A211225:=proc(q)

local b, i, n;

for n from 1 to q do

  b:=0;

  for i from 1 to trunc(n/2) do

    if sigma(i)+sigma(n-i)=sigma(n) then b:=b+1; fi;

  od;

  print(b)

od; end:

A211225(1000);

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

Cf. A083207, A204830, A204831, A211223, A211224.

Cf. A000203.

Sequence in context: A068101 A094263 A049761 * A030618 A025448 A015010

Adjacent sequences:  A211222 A211223 A211224 * A211226 A211227 A211228

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 07 2012

STATUS

approved

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Last modified September 17 09:04 EDT 2019. Contains 327128 sequences. (Running on oeis4.)