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

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, 41, 43, 44, 46, 47, 49, 53, 55, 56, 58, 59, 61, 62, 63, 67, 68, 70, 71, 73, 74, 75, 76, 78, 79, 80, 81, 83, 89, 90, 94, 95, 97, 98, 100, 101, 103, 104, 107, 109, 110

Offset

1,2

Comments

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.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Lee Troupe, Divisor sums representable as the sum of two squares, Proceedings of the American Mathematical Society, Vol. 148, No. 10 (2020), pp. 4189-4202.

Example

1 is a term since A001065(1) = 0 = 0^2 + 0^2.
9 is a term since A001065(9) = 4 = 0^2 + 2^2.

Mathematica

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

Crossrefs

Cf. A001065, A001481.

Sequence in context: A102246 A089743 A080587 * A175415 A304721 A063464

Adjacent sequences: A342187 A342188 A342189 * A342191 A342192 A342193

Keyword

nonn

Author

Amiram Eldar, Mar 04 2021

Status

approved