OFFSET
1,3
EXAMPLE
25 in base 2 is 11001 and its periodic derivative is (1+1)(1+0)(0+0)(0+1)(1+1) -> 01010 that is 10 in base 10 and 10 is also the arithmetic derivative of 25.
MAPLE
with(numtheory): P:=proc(q) local a, b, i, n, p;
for n from 0 to q do a:=0; b:=convert(n, base, 2); b:=[1, op(b)];
for i to nops(b)-1 do a:=a+((b[i]+b[i+1]) mod 2)*2^(i-1); od;
if a=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]) then print(n); fi;
od; end: P(10^6);
MATHEMATICA
Select[Range[0, 10^6], Function[n, If[Abs@ n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@ n]]] == FromDigits[Thread[BitXor[#, RotateLeft@ #]], 2] &@ IntegerDigits[n, 2]]] (* Michael De Vlieger, Jun 10 2016 after Michael Somos at A003415 and Jean-François Alcover at A038556 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jun 09 2016
EXTENSIONS
a(23)-a(31) from Giovanni Resta, Jun 19 2016
STATUS
approved