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A342190 Numbers k such that A001065(k) = sigma(k) - k is the sum of 2 squares. 1

%I

%S 1,2,3,5,7,9,10,11,12,13,14,15,17,19,23,24,26,27,29,31,34,35,37,39,40,

%T 41,43,44,46,47,49,53,55,56,58,59,61,62,63,67,68,70,71,73,74,75,76,78,

%U 79,80,81,83,89,90,94,95,97,98,100,101,103,104,107,109,110

%N Numbers k such that A001065(k) = sigma(k) - k is the sum of 2 squares.

%C Troupe (2020) proved that N(x), the number of terms not exceeding x, has an order of magnitude x/sqrt(x), i.e., there are two positive constants c1 and c2 such that c1*x/sqrt(x) < N(x) < c2*x/sqrt(x) for sufficiently large x.

%C All the primes are in this sequence since A001065(p) = 1 = 0^2 + 1^2 for a prime p.

%H Amiram Eldar, <a href="/A342190/b342190.txt">Table of n, a(n) for n = 1..10000</a>

%H Lee Troupe, <a href="https://doi.org/10.1090/proc/15104">Divisor sums representable as the sum of two squares</a>, Proceedings of the American Mathematical Society, Vol. 148, No. 10 (2020), pp. 4189-4202.

%e 1 is a term since A001065(1) = 0 = 0^2 + 0^2.

%e 9 is a term since A001065(9) = 4 = 0^2 + 2^2.

%t s[n_] := DivisorSigma[1, n] - n; Select[Range[100], SquaresR[2, s[#]] > 0 &]

%Y Cf. A001065, A001481.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 04 2021

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)