OFFSET
1,2
LINKS
EXAMPLE
The prime signature of 20 = 2^2*5 is (2,1). Since the largest number appearing in 20's prime signature is 2, and 1 appears as many times as 2, 20 is a member of this sequence.
MAPLE
isA179983 := proc(n)
local es, me, k ;
# list of exponents in prime signature
es := [seq(op(2, pe), pe =ifactors(n)[2])] ;
# maximum exponent
me := max(op(es)) ;
for k from me to 2 by -1 do
if numboccur(es, k-1) < numboccur(es, k) then
return false;
end if;
end do:
true ;
end proc:
for n from 1 to 100 do
if isA179983(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Mar 21 2023
MATHEMATICA
q[n_] := Module[{t = SortBy[Tally[FactorInteger[n][[;; , 2]]], First], t1, t2}, t1 = t[[;; , 1]]; t2 = t[[;; , 2]]; Sort[t1] == Range[Length[t1]] && Max[Differences[t2]] < 1]; Select[Range[100], q] (* Amiram Eldar, Aug 04 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jan 15 2011
STATUS
approved