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 A135572 A number n is included if the largest prime-power dividing n is a square. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1 is included in the sequence 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 included in the sequence. 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 *) CROSSREFS Cf. A034699. Sequence in context: A072587 A240112 A162645 * A337103 A312855 A312856 Adjacent sequences:  A135569 A135570 A135571 * A135573 A135574 A135575 KEYWORD nonn AUTHOR Leroy Quet, May 10 2008 EXTENSIONS More terms from R. J. Mathar, May 24 2008 STATUS approved

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Last modified November 27 04:07 EST 2020. Contains 338677 sequences. (Running on oeis4.)