A135572 - OEIS

%I #20 Jul 15 2022 15:04:35

%S 1,4,9,12,16,18,25,36,45,48,49,50,63,64,72,75,80,81,90,98,100,112,121,

%T 126,144,147,150,162,169,175,176,180,192,196,200,208,225,240,242,245,

%U 252,256,275,289,294,300,315,320,324,325,336,338,350,360,361,363,392

%N Numbers k such that the largest prime-power dividing k is a square.

%C 1 is a term because 1 is sometimes considered to be a prime-power.

%H Amiram Eldar, <a href="/A135572/b135572.txt">Table of n, a(n) for n = 1..10000</a>

%e The largest prime-power dividing 12 is 4. Since 4 is a square, then 12 is a term.

%e On the other hand, the largest prime-power dividing 24 is 8. Since 8 is not a square, then 24 is not in the sequence.

%p omega := proc(n) nops( numtheory[factorset](n)) ; end: isA000961 := proc(n) RETURN(n = 1 or omega(n) =1) ; end: A034699 := proc(n) local dvs,d ; dvs := sort(convert(numtheory[divisors](n),list),`>`) ; for d in dvs do if isA000961(d) then RETURN(d) ; fi ; od: end: isA135572 := proc(n) issqr(A034699(n)) ; end: for n from 1 to 800 do if isA135572(n) then printf("%d,",n) ; fi ; end: # _R. J. Mathar_, May 24 2008

%t Join[{1},Select[Range[400],IntegerQ[Sqrt[Max[Select[Divisors[#], PrimePowerQ]]]]&]] (* _Harvey P. Dale_, Aug 03 2017 *)

%t q[n_] := Module[{f = FactorInteger[n], i}, i = Ordering[Power @@@ f, -1][[1]]; EvenQ[f[[i, 2]]]]; Prepend[Select[Range[400], q], 1] (* _Amiram Eldar_, Jul 10 2022 *)

%Y Cf. A034699.

%K nonn

%O 1,2

%A _Leroy Quet_, May 10 2008

%E More terms from _R. J. Mathar_, May 24 2008