A174830 Odd numbers k such that k^2 is an abundant number.

105, 315, 495, 525, 585, 735, 945, 1155, 1365, 1485, 1575, 1755, 1785, 1995, 2145, 2205, 2415, 2475, 2625, 2805, 2835, 2925, 3045, 3135, 3255, 3315, 3465, 3675, 3705, 3795, 3885, 4095, 4305, 4455, 4485, 4515, 4725, 4785, 4845, 4935, 5115, 5145, 5265

Offset: 1

Author

Robert G. Wilson v, Mar 30 2010

Keywords

• nonn

Comments

Submitted at the suggestion of T. D. Noe.

For any number k, the abundance of k^2 is an odd number.

From Amiram Eldar, Jan 16 2025: (Start)

The least term that is not divisible by 5 is a(75) = 9009.

The least term that is not divisible by 3 is a(296889) = 37182145.

The least term that is coprime to 15 is 3909612711980232366109. (End)

The numbers of terms that do not exceed 10^k, for k = 3, 4, ..., are 7, 83, 792, 7988, 80082, 796603, 7952883, 79585351, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00795... . - Amiram Eldar, Apr 25 2025

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A005101, A005231, A033880, A156942.

Programs

Mathematica

fQ[n_] := Block[{ds = DivisorSigma[1, n^2] - 2 n^2}, ds > 0 && OddQ@ ds]; Select[ Range[1, 5353, 2], fQ@# &]

PARI

is(n)=n%2 && sigma(n^2,-1)>2 \\ Charles R Greathouse IV, Feb 21 2017

PARI

[2*k-1|k<-[1..6e3\2],sigma((2*k-1)^2,-1)>2] \\ M. F. Hasler, Jan 26 2020

Formula

a(n) = sqrt(A156942(n)). - M. F. Hasler, Jan 26 2020

Extensions

Name corrected by T. D. Noe, Jul 09 2010