The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307703 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A307703

Highly powerful numbers (A005934) that are not cubeful (A036966).
(history; published version)

#5 by N. J. A. Sloane at Tue May 07 15:17:43 EDT 2019

STATUS

proposed

approved

#4 by Amiram Eldar at Mon Apr 22 14:58:34 EDT 2019

STATUS

editing

proposed

#3 by Amiram Eldar at Mon Apr 22 14:52:21 EDT 2019

NAME

allocated for Amiram EldarHighly powerful numbers (A005934) that are not cubeful (A036966).

DATA

4, 144, 288, 86400, 129600, 194400, 259200, 518400, 190512000, 317520000, 381024000, 635040000, 9681819840000, 215982036990720000, 9466852651364908800000, 14200278977047363200000, 28400557954094726400000, 174294224164279335916800000, 522882672492838007750400000

OFFSET

1,1

COMMENTS

Lacampagne and Selfridge proved that these are the only terms.

The positions of the terms in A005934 are 2, 8, 10, 25, 27, 28, 30, 33, 55, 58, 60, 62, 107, 161, 230, 234, 240, 302, 315.

LINKS

Carole B. Lacampagne and John L. Selfridge, <a href="https://doi.org/10.1090/S0002-9939-1984-0740165-6">Large highly powerful numbers are cubeful</a>, Proceedings of the American Mathematical Society, Vol. 91, No. 2 (1984), pp. 173-181.

MATHEMATICA

pmax = 1; s = {}; Do[e = FactorInteger[n][[;; , 2]]; p = Times @@ e; If[p > pmax, pmax = p; If[Min[e] < 3, AppendTo[s, n]]], {n, 2, 10^6}]; s

CROSSREFS

Cf. A005934, A036966.

KEYWORD

allocated

nonn,fini,full

AUTHOR

Amiram Eldar, Apr 22 2019

STATUS

approved

editing

Discussion

Mon Apr 22

14:58

Amiram Eldar: With 261 characters, the full sequence perfectly fits the data section. Which is better: "cubeful" (as in the paper's title) or "cubefull" (as in A036966)?

#2 by Amiram Eldar at Mon Apr 22 14:52:21 EDT 2019

NAME

allocated for Amiram Eldar

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved