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%I #20 Sep 08 2022 08:46:19
%S 1,6,348,496,1420,1854,4674,5352,6424,13545,21126,28210,37336,57645,
%T 84370,95526,109648,116865,140056,150366,163450,176826,215430,305900,
%U 321496,330858,517914,558304,590790,617260,682746,742518,888550,927336,952938,1058344,1096758
%N Numbers k whose sum of divisors equals the sum of divisors of 2*k-1.
%C Most of the terms in this sequence are even.
%C Up to 10^7 there are 102 terms out of which 7 are odd.
%C There are two terms, 6 and 496, for which (2*k - 1) is a prime number.
%H Amiram Eldar, <a href="/A289738/b289738.txt">Table of n, a(n) for n = 1..1000</a>
%e 6 is in the sequence because the sum of divisors of 6: (1 + 2 + 3 + 6 = 12); equals the sum of divisors of 11 = 2*6 - 1: (1 + 11 = 12).
%e 348 is in the sequence because the sum of divisors of 348: (1 + 2 + 3 + 4 + 6 + 12 + 29 + 58 + 87 + 116 + 174 + 348 = 840); equals the sum of divisors of (2*348 - 1 = 695): (1 + 5 + 139 + 695 = 840).
%p with(numtheory): select(t -> sigma(t) = sigma(2*t-1), [$1..10^6]);
%t Select[Range[10^7], DivisorSigma[1, #] == DivisorSigma[1, 2 # - 1] &]
%o (PARI) for (n = 1, 1e7, (sigma(n)==sigma(2*n-1)) && print1(n ", "));
%o (Magma) [n : n in [1..10^6] | SumOfDivisors(n) eq SumOfDivisors(2*n-1)];
%Y Cf. A000203, A005101, A272553, A275370 (odd terms).
%K nonn
%O 1,2
%A _K. D. Bajpai_, Jul 10 2017
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