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A135572
Numbers k such that the largest prime-power dividing k is a square.
1
1, 4, 9, 12, 16, 18, 25, 36, 45, 48, 49, 50, 63, 64, 72, 75, 80, 81, 90, 98, 100, 112, 121, 126, 144, 147, 150, 162, 169, 175, 176, 180, 192, 196, 200, 208, 225, 240, 242, 245, 252, 256, 275, 289, 294, 300, 315, 320, 324, 325, 336, 338, 350, 360, 361, 363, 392
OFFSET
1,2
COMMENTS
1 is a term because 1 is sometimes considered to be a prime-power.
LINKS
EXAMPLE
The largest prime-power dividing 12 is 4. Since 4 is a square, then 12 is a term.
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.
MAPLE
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
MATHEMATICA
Join[{1}, Select[Range[400], IntegerQ[Sqrt[Max[Select[Divisors[#], PrimePowerQ]]]]&]] (* Harvey P. Dale, Aug 03 2017 *)
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 *)
CROSSREFS
Cf. A034699.
Sequence in context: A162645 A351575 A348739 * A337103 A312855 A348752
KEYWORD
nonn
AUTHOR
Leroy Quet, May 10 2008
EXTENSIONS
More terms from R. J. Mathar, May 24 2008
STATUS
approved