OFFSET
1,1
COMMENTS
If n = Product_{k=1..m} p(k)^e(k), then m > 1, e(1) >= e(2) >= ... >= e(m).
These are numbers whose ordered prime signature is weakly decreasing. Weakly increasing is A304678. Ordered prime signature is A124010. - Gus Wiseman, Nov 10 2019
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..20000
S. Ramanujan, Asymptotic formulas for the distribution of integers of various types, Proc. London Math. Soc. 2, 16 (1917), 112-132.
EXAMPLE
60 is 2^2*3^1*5^1, A001221(60)=3 and 2>=1>=1, so 60 is in sequence.
MAPLE
q:= n-> (l-> (t-> t>1 and andmap(i-> l[i, 2]>=l[i+1, 2],
[$1..t-1]))(nops(l)))(sort(ifactors(n)[2])):
select(q, [$1..120])[]; # Alois P. Heinz, Nov 11 2019
MATHEMATICA
fQ[n_] := Module[{f = Transpose[FactorInteger[n]][[2]]}, Length[f] > 1 && Max[Differences[f]] <= 0]; Select[Range[2, 200], fQ] (* T. D. Noe, Nov 04 2013 *)
PROG
(PARI) for(n=1, 130, 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", "))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, Aug 04 2004
STATUS
approved