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A349235 Numbers k such that k and k+4 are consecutive cubefree numbers. 3
1374, 4373, 4911, 5749, 6857, 13309, 13374, 16118, 21247, 24351, 25622, 28374, 31373, 32749, 33613, 40471, 41741, 48247, 49623, 49733, 52622, 55374, 57966, 58373, 59749, 75247, 76623, 79622, 82374, 85373, 86749, 90206, 94470, 98439, 102247, 103623, 106622, 107701 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 0.000379098586237504... (Mossinghoff et al., 2021).
LINKS
Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, The distribution of k-free numbers, Mathematics of Computation, Vol. 90, No. 328 (2021), pp. 907-929; arXiv preprint, arXiv:1912.04972 [math.NT], 2019-2020.
EXAMPLE
1374 is a term since 1374 = 2*3*229 and 1374 + 4 = 1378 = 2*13*53 are cubefree, and 1374 + 1 = 1375 = 5^3*11, 1374 + 2 = 1376 = 2^5*43 and 1374 + 3 = 1377 = 3^4*17 are not.
MATHEMATICA
cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[10^5], Boole[cubeFreeQ /@ (# + Range[0, 4])] == {1, 0, 0, 0, 1} &]
CROSSREFS
Sequence in context: A069490 A239974 A258964 * A045131 A365868 A056049
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 11 2021
STATUS
approved

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Last modified May 23 18:13 EDT 2024. Contains 372765 sequences. (Running on oeis4.)