OFFSET
1,2
COMMENTS
All terms are highly powerful (A005934), but that sequence looks only at first appearances that reach a record, and is missing 1152, 2048, 8192, etc.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wikipedia, Highly powerful number.
EXAMPLE
The prime exponents of 86400 are (7,3,2), and this is the first case of product 42, so 86400 is in the sequence.
MATHEMATICA
nn=1000;
d=Table[Times@@Last/@FactorInteger[n], {n, nn}];
Select[Range[nn], !MemberQ[Take[d, #-1], d[[#]]]&]
lps[fct_] := Module[{nf = Length[fct]}, Times @@ (Prime[Range[nf]]^Reverse[fct])]; lps[{1}] = 1; q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, (n == 1 || AllTrue[e, # > 1 &]) && n == Min[lps /@ f[Times @@ e]]]; Select[Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]], q] (* Amiram Eldar, Sep 29 2024, using the function f by T. D. Noe at A162247 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 17 2022
STATUS
approved