A209870 Numbers n for which tau(n) = tau(n'), where tau is the number of divisors of n and n' the arithmetic derivative of n.

4, 15, 21, 26, 27, 28, 33, 38, 48, 50, 57, 62, 69, 72, 74, 80, 85, 93, 99, 106, 129, 133, 134, 145, 156, 166, 176, 177, 178, 200, 205, 207, 213, 217, 218, 226, 237, 249, 253, 254, 262, 265, 276, 278, 308, 309, 314, 348, 362, 364, 368, 380, 393, 398, 410, 417

Offset: 1

Author

Paolo P. Lava, Mar 15 2012

Keywords

• nonn
• easy

Examples

			Divisors of 26 are four: 1, 2, 13 and 26. Arithmetic derivative of 26 is 15 and its divisors are four: 1, 3, 5 and 15.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A003415, A190402, A190403

Programs

Maple

with(numtheory);
A209870:=proc(n)
local a,i,p,pfs;
for i from 1 to n do
  pfs:=ifactors(i)[2]; a:=i*add(op(2,p)/op(1,p),p=pfs);
  if tau(a)=tau(i) then print(i); fi;
od; end:
A209870(1000);