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

1,1

Links

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

Example

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

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)

Crossrefs

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

Sequence in context: A201217 A041391 A245783 * A229015 A324318 A058196

Adjacent sequences: A189054 A189055 A189056 * A189058 A189059 A189060

Keyword

nonn

Author

Paolo P. Lava, May 17 2011

Status

approved