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A060859 Powerful numbers of the form k^2 - 1. 5
8, 288, 675, 9800, 235224, 332928, 1825200, 11309768, 384199200, 592192224, 4931691075, 13051463048, 221322261600, 443365544448, 865363202000, 8192480787000, 13325427460800, 15061377048200, 511643454094368 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
If k^2-1 is a term, then k-1 is a term of A335851. - Amiram Eldar, Feb 23 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..55 (terms below 10^36; terms 1..30 from Donovan Johnson)
FORMULA
a(n) = k^2 - 1 and a(n) + 1 = k^2 are consecutive powerful numbers.
a(n) = A060860(n)^2 - 1. - Amiram Eldar, Feb 23 2024
EXAMPLE
From Jon E. Schoenfield, Sep 06 2017: (Start)
n k a(n) = k^2 - 1 a(n) + 1 = k^2
= === ========================= ==================
1 3 8 = 2^3 3^2 = 3^2
2 17 288 = 2^5 * 3^2 17^2 = 17^2
3 26 675 = 5^2 * 3^3 26^2 = 2^2 * 13^2
4 99 9800 = 2^3 * 5^2 * 7^2 99^2 = 3^4 * 11^2
5 485 235224 = 2^3 * 3^5 * 11^2 485^2 = 5^2 * 97^2
6 577 332928 = 2^7 * 3^2 * 17^2 577^2 = 577^2
(End)
MATHEMATICA
Select[Range[10^6]^2 - 1, Min[FactorInteger[#][[All, -1]]] > 1 &] (* Michael De Vlieger, Sep 05 2017 *)
seq[max_] := Module[{p = Union[Flatten[Table[i^2*j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}]]], q, i}, q = Union[p, 2*Select[p, # <= max && OddQ[#] &]]; i = Position[Differences[q], 2] // Flatten; q[[i]]*(q[[i]] + 2)]; seq[10^10] (* Amiram Eldar, Feb 23 2024 *)
PROG
(PARI) isok(n) = issquare(n+1) && ispowerful(n); \\ Michel Marcus, Sep 05 2017
CROSSREFS
Proper subset of A060355.
Sequence in context: A221612 A348122 A060355 * A187289 A187191 A054607
KEYWORD
nonn
AUTHOR
Labos Elemer, May 04 2001
EXTENSIONS
Corrected and extended by Jud McCranie, Jul 08 2001
Offset corrected by Donovan Johnson, Nov 15 2011
Name simplified by Jon E. Schoenfield, Nov 30 2023
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)