A351220 Numbers k such that sigma(L(k)) > 2*L(K), where L(k) is the k-th Lucas number.

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

Amiram Eldar, Table of n, a(n) for n = 1..142

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

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

Sequence in context: A077660 A240991 A304050 * A242394 A030568 A017593

Adjacent sequences: A351217 A351218 A351219 * A351221 A351222 A351223

Keyword

nonn

Author

Amiram Eldar, Feb 05 2022

Status

approved