A158276 Numbers k such that sigma_1(k) does not divide sigma_2(k).

2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77

Offset

1,1

Comments

Numbers k such that the antiharmonic mean of divisors of k is not an integer.

Antiharmonic mean of divisors of a number m = Product (p_i^e_i) is A001157(m)/A000203(m) = Product ((p_i^(e_i+1)+1)/(p_i+1)).

Numbers k such that A001157(k)/A000203(k) is not an integer.

Links

Table of n, a(n) for n=1..67.

Example

a(12) = 15, sigma_2(15)/sigma_1(15)=260/24 = 65/6 (not integer).

Mathematica

Select[Range[100], Mod @@ DivisorSigma[{2, 1}, #] > 0 &] (* Amiram Eldar, Mar 22 2024 *)

Prog

(PARI) is(n) ={my(f = factor(n)); sigma(f, 2) % sigma(f); } \\ Amiram Eldar, Mar 22 2024

Crossrefs

Complement of A020487.

Cf. A001157, A000203.

Sequence in context: A028797 A028773 A028813 * A028793 A028753 A336918

Adjacent sequences: A158273 A158274 A158275 * A158277 A158278 A158279

Keyword

nonn

Author

Jaroslav Krizek, Mar 15 2009

Extensions

More terms from Amiram Eldar, Mar 22 2024

Status

approved