

A333911


Numbers k such that sigma(k) is the sum of 2 squares, where sigma is the sum of divisors function (A000203).


3



1, 3, 7, 9, 10, 17, 19, 21, 22, 27, 30, 31, 40, 46, 51, 52, 55, 57, 58, 63, 66, 67, 70, 71, 73, 79, 81, 88, 89, 90, 93, 94, 97, 103, 106, 115, 118, 119, 120, 127, 133, 138, 145, 153, 154, 156, 163, 165, 170, 171, 174, 179, 184, 189, 190, 193, 198, 199, 201, 202
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OFFSET

1,2


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000
William D. Banks, Florian Luca, Filip Saidak, and Igor E. Shparlinski, Values of arithmetical functions equal to a sum of two squares, Quarterly Journal of Mathematics, Vol. 56, No. 2 (2005), pp. 123139, alternative link.


FORMULA

c1 * x/log(x)^(3/2) < N(x) < c2 * x/log(x)^(3/2), where N(x) is the number of terms <= x, and c1 and c2 are two positive constants (Banks et al., 2005).


EXAMPLE

1 is a term since sigma(1) = 1 = 0^2 + 1^2.


MATHEMATICA

Select[Range[200], SquaresR[2, DivisorSigma[1, #]] > 0 &]


CROSSREFS

Cf. A000203, A001481, A079545, A272405, A333909, A333910.
Sequence in context: A294571 A083214 A091210 * A276492 A023992 A179197
Adjacent sequences: A333908 A333909 A333910 * A333912 A333913 A333914


KEYWORD

nonn


AUTHOR

Amiram Eldar, Apr 09 2020


STATUS

approved



