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A332785 Nonsquarefree numbers that are not squareful. 0
12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 75, 76, 80, 84, 88, 90, 92, 96, 98, 99, 104, 112, 116, 117, 120, 124, 126, 132, 135, 136, 140, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 198, 204, 207, 208, 212, 220, 224 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sometimes nonsquarefree numbers are misnamed squareful numbers (see 1st comment of A013929). Indeed, every squareful number > 1 is nonsquarefree, but the converse is false. This sequence = A013929 \ A001694 and consists of these counterexamples.

This sequence is not a duplicate: the first 16 terms (<= 68) are the same first 16 terms of A059404, A323055, A242416 and A303946, then 72 is the 17th term of these 4 sequences. Also, the first 37 terms (<= 140) are the same first 37 terms of A317616 then 144 is the 38th term of this last sequence.

LINKS

Table of n, a(n) for n=1..63.

EXAMPLE

18 = 2 * 3^2 is nonsquarefree as it is divisible by the square 3^2, but it is not squareful because 2 divides 18 but 2^2 does not divide 18, hence 18 is a term.

72 = 2^3 * 3^2 is nonsquarefree as it is divisible by the square 3^2, but it is also squareful because primes 2 and 3 divide 72, and 2^2 and 3^2 divide also 72, so 72 is not a term.

MATHEMATICA

Select[Range[225], Max[(e = FactorInteger[#][[;; , 2]])] > 1 && Min[e] == 1 &] (* Amiram Eldar, Feb 24 2020 *)

PROG

(PARI) isok(m) = !issquarefree(m) && !ispowerful(m); \\ Michel Marcus, Feb 24 2020

CROSSREFS

Cf. A005117 (squarefree), A013929 (nonsquarefree), A001694 (squareful), A052485 (not squareful).

Cf. A059404, A242416, A303946, A317616, A323055 (first terms are the same).

Sequence in context: A303946 A242416 A317616 * A177425 A182854 A328930

Adjacent sequences:  A332782 A332783 A332784 * A332786 A332787 A332788

KEYWORD

nonn

AUTHOR

Bernard Schott, Feb 24 2020

STATUS

approved

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Last modified September 26 05:00 EDT 2020. Contains 337346 sequences. (Running on oeis4.)