A144922 Numbers k such that k*sigma_2(k)/sigma_1(k) is an integer

1, 4, 6, 9, 12, 16, 18, 20, 24, 25, 28, 36, 44, 45, 48, 49, 50, 54, 60, 64, 72, 81, 90, 92, 96, 100, 108, 112, 117, 121, 132, 140, 144, 150, 153, 162, 168, 169, 180, 192, 196, 198, 200, 204, 216, 225, 228, 234, 240, 242, 252, 256, 270, 288, 289, 294, 300

Offset

1,2

Comments

Numbers k such that k*A001157(k)/A000203(k) is an integer. This sequence is connected closely with Ore divisor numbers (A001599) and RMS numbers (A140480).

This sequence is infinite. E.g., all the numbers of the form 3*2^m, for m >= 1, are terms, since 3*2^m * sigma_2(3*2^m) / sigma_1(3*2^m) = 5 * 2^(m-1) * (2^(m+1)+1) is an integer. - Amiram Eldar, Dec 25 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Mathematica

Select[Range[300], IntegerQ[(#*DivisorSigma[2, #])/DivisorSigma[1, #]]&] (* Harvey P. Dale, Oct 28 2018 *)

Prog

(PARI) is(k) = my(f = factor(k)); !((k*sigma(f, 2)) % sigma(f)); \\ Amiram Eldar, Dec 25 2024

Crossrefs

Cf. A000203, A001157, A001599, A140480.

A020487 is a subsequence.

Sequence in context: A163656 A134678 A100915 * A298864 A310667 A317538

Adjacent sequences: A144919 A144920 A144921 * A144923 A144924 A144925

Keyword

easy,nonn

Author

Ctibor O. Zizka, Sep 25 2008

Extensions

More terms from Harvey P. Dale, Oct 28 2018

Status

approved