A189057 Numbers n for which phi(n)=sigma(n'), where phi is the Euler totient function, sigma is the sum of divisors and n' the arithmetic derivative of n.

2, 57, 175, 357, 381, 543, 777, 903, 2379, 3027, 6807, 25823, 47047, 74333, 82621, 136213, 153425, 163471, 194873, 230547, 257799, 259555, 265111, 269545, 285439, 289009, 302403, 305305, 311395, 354365, 416005, 484169, 569245, 718333, 755885, 781501, 1012505

Offset: 1

Author

Paolo P. Lava, May 17 2011

Keywords

• nonn

Examples

			phi(57)=36. 57'=22 and sigma(22)=36
phi(1012505)=725760. 1012505'=310156 and sigma(310156)=725760
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000010, A000203, A003415, A166374, A190402, A190403.

Programs

Maple

with(numtheory);
P:=proc(i)
local f, n, p, pfs;
for n from 1 by 1 to i do
    pfs:=ifactors(n)[2];
    f:=n*add(op(2, p)/op(1, p), p=pfs);
    if phi(n)=sigma(f) then print(n); fi;
od;
end:
P(1000000)