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

1,39

Links

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

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);

Crossrefs

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

Sequence in context: A016380 A341354 A203945 * A341774 A015692 A016232

Adjacent sequences: A212660 A212661 A212662 * A212664 A212665 A212666

Keyword

nonn

Author

Paolo P. Lava, May 23 2012

Status

approved