A212663 Number of ways to represent n’ as x’ + y’, where x+y = n, x > 0, and n’, x’, y’ are the arithmetic derivatives of n, x, y.

0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 1, 2, 0, 1

Offset: 1

Author

Paolo P. Lava, May 23 2012

Keywords

• nonn

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A003415, A211223-A211225, A212662, A212664.

Programs

Maple

with(numtheory);
A212663:=proc(q)
local a,b,c,i,n,p,pfs,t;
for n from 1 to q do
  pfs:=ifactors(n)[2]; a:=n*add(op(2,p)/op(1,p),p=pfs); t:=0;
  for i from 1 to trunc(n/2) do
   pfs:=ifactors(i)[2]; b:=i*add(op(2,p)/op(1,p),p=pfs);
   pfs:=ifactors(n-i)[2]; c:=(n-i)*add(op(2,p)/op(1,p),p=pfs);
   if a=b+c then t:=t+1; fi;
  od;
  print(t);
od; end:
A212663(1000);