A373437 Integers k such that sigma(sigma(2*k))=2*sigma(sigma(k)); sigma=A000203.

2, 6, 14, 18, 38, 42, 50, 54, 62, 74, 86, 114, 122, 126, 134, 146, 150, 158, 162, 186, 206, 218, 222, 254, 258, 266, 302, 314, 326, 342, 350, 366, 378, 386, 398, 402, 422, 434, 438, 450, 458, 474, 482, 518, 542, 554, 558, 566, 578, 602, 618, 626, 654, 662, 666, 674, 686, 734, 746, 758, 762, 774, 794

Offset: 1

Author

Rafik Khalfi, Jun 04 2024

Keywords

• nonn

Links

• Graeme L. Cohen and H. J. J. te Riele, Iterating the sum-of-divisors function, Exp. Math., 5 (1996), 91-100.

Crossrefs

Cf. A000203, A051027.

Programs

Maple

with(numtheory):
P := proc (q)
    local n, result:
    result := []:
    for n to q do
        if sigma(sigma(2*n)) = 2*sigma(sigma(n)) then
            result := [op(result), n]:
        end if
    end do:
    print(result):
end proc:
P(10^3);

Mathematica

Select[Range[800],DivisorSigma[1,DivisorSigma[1,2#]]==2DivisorSigma[1,DivisorSigma[1,#]]&] (* Stefano Spezia, Jun 05 2024 *)

Python

from sympy import divisor_sigma as sigma
def P(q):
    result = []
    for n in range(1, q + 1):
        if sigma(sigma(2 * n)) == 2 * sigma(sigma(n)):
            result.append(n)
    print(result)
P(10**3)