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

Author

Ctibor O. Zizka, Sep 25 2008

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A000203, A001157, A001599, A140480.

A020487 is a subsequence.

Programs

Mathematica

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

PARI

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

Extensions

More terms from Harvey P. Dale, Oct 28 2018