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

%I A373437 #18 Jun 22 2024 15:48:37
%S A373437 2,6,14,18,38,42,50,54,62,74,86,114,122,126,134,146,150,158,162,186,
%T A373437 206,218,222,254,258,266,302,314,326,342,350,366,378,386,398,402,422,
%U A373437 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
%N A373437 Integers k such that sigma(sigma(2*k))=2*sigma(sigma(k)); sigma=A000203.
%H A373437 Graeme L. Cohen and H. J. J. te Riele, <a href="https://doi.org/10.1080/10586458.1996.10504580">Iterating the sum-of-divisors function</a>, Exp. Math., 5 (1996), 91-100.
%p A373437 with(numtheory):
%p A373437 P := proc (q)
%p A373437     local n, result:
%p A373437     result := []:
%p A373437     for n to q do
%p A373437         if sigma(sigma(2*n)) = 2*sigma(sigma(n)) then
%p A373437             result := [op(result), n]:
%p A373437         end if
%p A373437     end do:
%p A373437     print(result):
%p A373437 end proc:
%p A373437 P(10^3);
%t A373437 Select[Range[800],DivisorSigma[1,DivisorSigma[1,2#]]==2DivisorSigma[1,DivisorSigma[1,#]]&] (* _Stefano Spezia_, Jun 05 2024 *)
%o A373437 (Python)
%o A373437 from sympy import divisor_sigma as sigma
%o A373437 def P(q):
%o A373437     result = []
%o A373437     for n in range(1, q + 1):
%o A373437         if sigma(sigma(2 * n)) == 2 * sigma(sigma(n)):
%o A373437             result.append(n)
%o A373437     print(result)
%o A373437 P(10**3)
%Y A373437 Cf. A000203, A051027.
%K A373437 nonn
%O A373437 1,1
%A A373437 _Rafik Khalfi_, Jun 04 2024