The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A372296 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A372296

Taxicab numbers that are sandwiched between nonsquarefree numbers.
(history; published version)

#10 by N. J. A. Sloane at Sun May 19 12:02:34 EDT 2024

STATUS

proposed

approved

#9 by Amiram Eldar at Thu Apr 25 11:18:01 EDT 2024

STATUS

editing

proposed

#8 by Amiram Eldar at Thu Apr 25 11:17:57 EDT 2024

NAME

Taxicab numbers that are sandwiched between no squarefree nonsquarefree numbers.

REFERENCES

Christian Boyer, Les nombres Taxicabs, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

LINKS

Christian Boyer, <a href="https://medias.pourlascience.fr/api/v1/files/5a82a1e48fe56f68674f7ff2?alt=file">Les nombres Taxicabs</a>, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

#7 by Amiram Eldar at Thu Apr 25 11:17:10 EDT 2024

CROSSREFS

Cf. A001235, A011541, A013929, A371602.

#6 by Amiram Eldar at Thu Apr 25 11:16:50 EDT 2024

MATHEMATICA

Select[Import["https://oeis.org/A001235/b001235.txt", "Table"][[;; , 2]], # < 3*10^7 && Nor @@ SquareFreeQ /@ (# + {-1, 1}) &] (* Amiram Eldar, Apr 25 2024 *)

CROSSREFS

Cf. A001235, A011541, A013929.

STATUS

proposed

editing

#5 by Massimo Kofler at Thu Apr 25 11:13:27 EDT 2024

STATUS

editing

proposed

#4 by Massimo Kofler at Thu Apr 25 11:12:57 EDT 2024

DATA

20683, 216125, 327763, 593047, 684019, 842751, 1061424, 1845649, 2691451, 4505949, 4744376, 5004125, 5772403, 6058747, 7640128, 8029000, 8216000, 8494577, 10702783, 10765603, 10821896, 11859211, 12533824, 13731319, 14916727, 16776487, 18406603, 18617625, 20616463, 22031576, 24480125, 25937576, 27529073

STATUS

proposed

editing

#3 by Massimo Kofler at Thu Apr 25 10:35:16 EDT 2024

STATUS

editing

proposed

Discussion

Thu Apr 25

10:56

Hugo Pfoertner: I don't know how well-defined "sandwiched between ..." is.  I would prefer "Taxicab numbers k such that k-1 and k+1 are not squarefree".

11:04

Massimo Kofler: Tks Hugo Pfoertner. I just used the same form that has been approved in A371602.

11:04

Amiram Eldar: Why is 1061424 a term? 1061424 - 1 = 1061423 = 11 * 96493 is squarefree.

11:08

Massimo Kofler: Tks Amiram Eldar. My mistake.

#2 by Massimo Kofler at Thu Apr 25 10:34:27 EDT 2024

NAME

allocated for Massimo KoflerTaxicab numbers that are sandwiched between no squarefree numbers.

DATA

OFFSET

1,1

REFERENCES

Christian Boyer, Les nombres Taxicabs, in Dossier Pour La Science, pp. 26-28, Volume 59 (Jeux math') April/June 2008 Paris.

EXAMPLE

20683 = 13 ⋅ 37 ⋅ 43 (between 20682 = 2 ⋅ 3^3 ⋅ 383 and 20684 = 2^2 ⋅ 5171).

216125 = 5^3 ⋅ 7 ⋅ 13 ⋅ 19 (between 216124 = 2^2 ⋅ 71 ⋅ 761 and 216126 = 2 ⋅ 3^2 ⋅ 12007).

327763 = 31 ⋅ 37 ⋅ 109 (between 327762 = 2 ⋅ 3^2 ⋅ 131 ⋅ 139 and 327764 = 2^2 ⋅ 67 ⋅ 1223).

CROSSREFS

Cf. A011541, A013929.

KEYWORD

allocated

nonn

AUTHOR

Massimo Kofler, Apr 25 2024

STATUS

approved

editing

#1 by Massimo Kofler at Thu Apr 25 10:34:27 EDT 2024

NAME

allocated for Massimo Kofler

KEYWORD

allocated

STATUS

approved