OFFSET
1,1
COMMENTS
If n = Product_{k=1..m} p(k)^e(k), then m > 1, e(1) > e(2) > ... > e(m).
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
EXAMPLE
80 is 2^4 * 5^1 and 4>1, so 80 is in sequence.
MATHEMATICA
fQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Length[f] > 1 && Max[Differences[f]] < 0]; Select[Range[2, 288], fQ] (* T. D. Noe, Nov 04 2013 *)
PROG
(PARI) for(n=1, 320, F=factor(n); t=0; s=matsize(F)[1]; if(s>1, for(k=1, s-1, if(F[k, 2]<=F[k+1, 2], t=1; break)); if(!t, print1(n", "))))
(PARI) is(n) = my(f = factor(n)[, 2]); #f > 1 && vecsort(f, , 12) == f \\ Rick L. Shepherd, Jan 17 2018
(Python)
from sympy import factorint
def ok(n):
e = list(factorint(n).values())
return 1 < len(e) == len(set(e)) and e == sorted(e, reverse=True)
print([k for k in range(289) if ok(k)]) # Michael S. Branicky, Dec 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 04 2004
STATUS
approved