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

1,1

Links

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

Example

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.

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);

Crossrefs

Cf. A000005, A003415, A190402, A190403

Sequence in context: A170850 A297711 A055465 * A167293 A267769 A192201

Adjacent sequences: A209867 A209868 A209869 * A209871 A209872 A209873

Keyword

nonn,easy

Author

Paolo P. Lava, Mar 15 2012

Status

approved