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A351220
Numbers k such that sigma(L(k)) > 2*L(K), where L(k) is the k-th Lucas number.
1
6, 18, 30, 42, 45, 54, 66, 75, 78, 90, 102, 105, 114, 126, 135, 138, 150, 162, 165, 174, 186, 195, 198, 210, 222, 225, 234, 246, 258, 270, 282, 294, 306, 315, 318, 330, 342, 354, 366, 375, 378, 390, 402, 405, 414, 426, 435, 438, 450, 462, 474, 486, 495, 498, 510
OFFSET
1,1
COMMENTS
Indices of Lucas numbers that are abundant numbers (A005101).
The asymptotic density of this sequence is larger than 71/700 = 0.1014... (Wall, 1982).
LINKS
Charles R. Wall, Problem H-338, Advanced Problems and Solutions, The Fibonacci Quarterly, Vol. 20, No. 1 (1982), p. 94; Some Abundance, Solution to Problem H-338 by the proposer, ibid., Vol. 21, No. 2 (1983), pp. 159-160.
MATHEMATICA
Select[Range[0, 250], DivisorSigma[-1, LucasL[#]] > 2 &]
PROG
(Python) from sympy import divisor_sigma, lucas
print([k for k in range(150) if divisor_sigma(lucas(k)) > 2*lucas(k)])
# Karl-Heinz Hofmann, Feb 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 05 2022
STATUS
approved