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%I #21 Jun 18 2026 08:45:55
%S 1,65,175,525,1105,5425,16275,20737,30225,32045,70525,86025,103685,
%T 171275,200725,207553,211575,352529,372775,474075,513825,602175,
%U 1037765,1118325,1198925,1264957,1347905,1555275,1762645,1824877,2436525,2609425,2698189,3596775
%N Odd numbers k where sigma_2(k)/k is an integer.
%H Alexander Violette, <a href="/A396599/b396599.txt">Table of n, a(n) for n = 1..104</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Divisor_function">Divisor function</a>.
%e 65's divisors are 1, 5, 13, and 65. Since (1^2+5^2+13^2+65^2)/65 is an integer, 65 is in this sequence.
%t Select[Range[1, 4000000, 2], Divisible[DivisorSigma[2, #], #] &] (* _Amiram Eldar_, Jun 03 2026 *)
%o (PARI) isok(k) = (k%2) && (denominator(sigma(k, 2)/k) == 1); \\ _Michel Marcus_, Jun 03 2026
%Y Intersection of A005408 and A046762.
%Y Cf. A000203, A001157, A396600, A396601, A396602.
%K nonn
%O 1,2
%A _Alexander Violette_, May 30 2026