

A135572


A number n is included if the largest primepower 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 primepower.


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

The largest primepower dividing 12 is 4. Since 4 is a square, then 12 is included in the sequence. On the other hand, the largest primepower 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



