OFFSET
1,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..609 (terms 1..300 from T. D. Noe)
G. E. Hardy and M. V. Subbarao, Highly powerful numbers, Congress. Numer., Vol. 37 (1983), pp. 277-307. (Annotated scanned copy)
C. B. Lacampagne and J. L. Selfridge, Large highly powerful numbers are cubeful, Proc. Amer. Math. Soc., Vol. 91, No. 2 (1984), pp. 173-181.
Wikipedia, Highly powerful number.
FORMULA
For n = Product p_i^e_i, let b(n) = Product e_i; then n is highly powerful if b(n) sets a new record.
MATHEMATICA
a = {1}; b = {1}; f[n_] := Times @@ Last /@ FactorInteger[n]; Do[If[f@ n > Max[b], And[AppendTo[b, f@ n], AppendTo[a, n]]], {n, 1000000}]; a (* Michael De Vlieger, Aug 28 2015 *)
With[{s = Array[Times @@ FactorInteger[#][[All, -1]] &, 3*10^6]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Oct 15 2017 *)
DeleteDuplicates[Table[{n, Times@@FactorInteger[n][[All, 2]]}, {n, 26*10^5}], GreaterEqual[#1[[2]], #2[[2]]]&][[All, 1]] (* Harvey P. Dale, May 13 2022 *)
PROG
(PARI) {prdex(n)=local(s, fac); s=1; fac=factor(n); for(k=1, matsize(fac)[1], s=s*fac[k, 2]); return(s)} {hp(m)=local(rec); rec=0; for(n=1, m, if(prdex(n)>rec, rec=prdex(n); print1(n", ")))}
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Hardy and Subbarao give an extensive table.
Corrected and extended by Jason Earls, Jul 10 2003
STATUS
approved