A351220 - OEIS

%I #22 Jan 05 2025 19:51:42

%S 6,18,30,42,45,54,66,75,78,90,102,105,114,126,135,138,150,162,165,174,

%T 186,195,198,210,222,225,234,246,258,270,282,294,306,315,318,330,342,

%U 354,366,375,378,390,402,405,414,426,435,438,450,462,474,486,495,498,510

%N Numbers k such that sigma(L(k)) > 2*L(K), where L(k) is the k-th Lucas number.

%C Indices of Lucas numbers that are abundant numbers (A005101).

%C The asymptotic density of this sequence is larger than 71/700 = 0.1014... (Wall, 1982).

%H Amiram Eldar, <a href="/A351220/b351220.txt">Table of n, a(n) for n = 1..142</a>

%H Charles R. Wall, <a href="https://fq.math.ca/Scanned/20-1/advanced20-1.pdf">Problem H-338</a>, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 20, No. 1 (1982), p. 94; <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/21-2/advanced21-2.pdf">Some Abundance</a>, Solution to Problem H-338 by the proposer, ibid., Vol. 21, No. 2 (1983), pp. 159-160.

%t Select[Range[0, 250], DivisorSigma[-1, LucasL[#]] > 2 &]

%o (Python) from sympy import divisor_sigma, lucas

%o print([k for k in range(150) if divisor_sigma(lucas(k)) > 2*lucas(k)])

%o # _Karl-Heinz Hofmann_, Feb 07 2022

%Y Cf. A000032, A000203, A005101, A074726, A272439.

%K nonn

%O 1,1

%A _Amiram Eldar_, Feb 05 2022